# Find a set of 4 distinct positive integers a,b,c,d such that the smallest positive integer that can not be represented by such expressions involving a,b,c,d (instead of 1,2,3,4) is greater than 22.You can use digits exactly once. You are allowed

117,263 results
1. ## discrete math

Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.

2. ## mathematics

Let P(x) be a nonconstant polynomial, where all the coefficients are nonnegative integers. Prove that there exist infinitely many positive integers n such that P(n) is composite. Remember that if a and b are distinct integers, then P(a) - P(b) is divisible

3. ## Algebra

The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers. Must have an algebraic solution.

4. ## algebra 1

Find three positive consecutive integers such that the product of the second integer and the third integer is 72.

5. ## math

Find the smallest positive integer not relatively prime to 2015 that has the same number of positive divisors as 2015.

6. ## Integers

The larger of two positive integers is five more than twice the smaller integer. The product of the integers is 52. Find the integers.

7. ## Math

Tell whether the difference between the two integers is always, sometimes, or never positive. 1)Two positive integers. Never 2)Two negative integers. Sometimes. 3)A positive integer and a negative integer. Sometimes. 4)A negative integer and positive

8. ## math , probability

Let X and Y be two independent and identically distributed random variables that take only positive integer values. Their PMF is px (n) = py (n) = 2^-n for every n e N, where N is the set of positive integers. 1. Fix at E N. Find the probability P

9. ## Discrete Math

Theorem: For every integer n, if x and y are positive integers with max(x, y) = n, then x = y. Basic Step: Suppose that n = 1. If max(x, y) = 1 and x and y are positive integers, we have x = 1 and y = 1. Inductive Step: Let k be a positive integer. Assume

10. ## Math

The squares of three positive integers are in arithmetic progression, and the third integer is 12 greater than the first. Find the second integer.

11. ## Math

find three consecutive positive odd integers such that the sum of the squares of the first and second integers is equal to the square of the third integer minus 7?

12. ## discrete math

1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive? For 1) use the definition of

13. ## math

Which statement is true? A.The sum of two positive integers is sometimes positive, sometimes negative. B.The sum of two negative integers is always negative. C.The sum of a positive integer and a negative integer is always positive. D.The sum of a positive

14. ## Algebra

find three consecutive positive even integers such that the product of the second and third integers is twenty more than ten times the first integer. [only an algebraic solution can give full credit]

15. ## algebra

Find two consecutive positive integers such that the sum of their squares is 85. n^2+(n+1)^2+2n = 85 n^2+n^2+2n+1=85 2n^2+2n=84 n^2+n=42 n^2+n-42=0 (n-6)(n+7)=0 n=6 n=-7 Is my work and answer correct? -7 is not a positive integer. Your first equation is

16. ## smallest of 3 integers

The sum of the reciprocals of three consecutive positive integers is equal to 47 divided by the product of the integers. What is the smallest of the three integers?

17. ## Math

I suggest if you cannot check them please don't comment. Not trying to be rude but pretty sure most u know what I mean. I am not here for answers just for someone to check my work 6th grade math. 1. -15 > -21 A. > B. < C. = Which number is greater than -24

18. ## Math

Find four consecutive,positive,even integers such that the product of the and the last integer equals the square of the 2nd integers

19. ## maths

the non- decreasing sequence of odd integers {a1, a2, a3, . . .} = {1,3,3,3,5,5,5,5,5,...} each positive odd integer k appears k times. it is a fact that there are integers b, c, and d such that, for all positive integers n, añ = b[√(n+c)] +d. Where [x]

20. ## MAth

In a set of five consecutive positive even integers, the ratio of the greatest integer to least integer is 2 is to 1. If these integers are arranged from lowest to highest, which is the middle integer in the list?

21. ## heeeelp math

For each positive integer n, let Hn=1/1 + 1/2 +⋯+ 1/n . If ∑ (up)∞ (base)(n=4) 1/n*Hn*H(n-1)= a/b for relatively prime positive integers a and b, find a+b.

22. ## Math

Find the smallest positive integer n such that sqrtx-sqrt(x-1)

23. ## MATH

Find the only positive integer whose cube is the sum of the cubes of three positive integers immediately preceding it. Find this positive integer. Your algebraic work must be detailed enough to show this is the only positive integer with this property

24. ## Math

Find the smallest positive integer d such that d=105m+216n, where m & n are integers.

25. ## Math

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? I can't remember how to start this.

26. ## Math

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? I can't remember how to start this.

27. ## Maths

A give an example of a function whose domain equals the set of real numbers and whose range equals the set? the set {-1,0,1} BGive an example of a function whose domain equals (0,1)and whose range equals [0,1] C.Give n example of a function whose is the

28. ## maths

The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?

29. ## calculus

A positive multiple of 11 is good if it does not contain any even digits in its decimal representation. (a) Find the number of good integers less than 1000. (b) Determine the largest such good integer. (c) Fix b ≥ 2 an even integer. Find the number of

30. ## math

Let S={1,2,3,4,…,2013} and let n be the smallest positive integer such that the product of any n distinct elements in S is divisible by 2013. What are the last 3 digits of n?

31. ## Math

1. Set I contains six consecutive integers. Set J contains all integers that result from adding 3 to each of the integers in set I and also contains all integers that result from subtracting 3 from each of the integers in set I. How man more integers are

32. ## arithmetic

Find the smallest positive integer P such that the cube root of 400 times P is an integer.

33. ## math

Suppose A,B,C,D and E are distinct positive integers such that A < B < C < D < E,their median is 10 and their mean is 15.Find the maximum possible value of D.

34. ## math

the sum of the reciprocals of three consecutive positive integers is equal to 47 divided by the product of the integers. what is the smallest of the three integers?

35. ## math

1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,

36. ## MATH combinatorics HELP!!!!!

Determine the least positive integer n for which the following condition holds: No matter how the elements of the set of the first n positive integers, i.e. {1,2,…n}, are colored in red or blue, there are (not necessarily distinct) integers x,y,z, and w

37. ## math

there are three consecutive positive integers such that the sum of the squares of the smallest two is 221. write and equation to find the three consecutive positive integers let x= the smallest integer

38. ## math

Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not divisible by any prime less

39. ## Math

Paulo withdraws the same amount from his bank account each week to pay for lunch. Over the past four weeks, he withdrew one hundred twenty dollars. Which rule best applies to determine the change in his account each week? 1. The product of two positive

40. ## math, algebra

2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure this out. Let n be a

41. ## Math

A smooth partition of the integer n is a set of positive integers a 1 ,a 2 ,…a k such that 1. k is a positive integer, 2. a 1 ≤a 2 ≤⋯≤a k , 3. ∑ k i=1 a i =n, and 4. a k −a 1 ≤1. Determine how many smooth partitions there are of the integer

42. ## Number theroy

What is the 50th smallest positive integer that can be written as the sum of distinct non-negative integer powers of 3?

43. ## Math

Find the smallest positive integer n such that the equation 455x+1547y=50,000+n has a solution (x,y) where both x and y are integers

44. ## mathematics

4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of p/q+r/s can be written as ab, where a and b are positive, coprime integers. What is the value of a+b?

45. ## Math

Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?

46. ## math

I do not undeerstand this question for homework. Determine if the set is closed for the given operation. 1. yes or no- The set of positive fractions for division. 2. yes or no=The set of positive integers for subtraction. Can someone help me?

47. ## Discrete Math

Let n be positive integer greater than 1. We call n prime if the only positive integers that (exactly) divide n are 1 and n itself. For example, the first seven primes are 2, 3, 5, 7, 11, 13 and 17. (We should learn more about primes in Chapter 4.) Use the

48. ## Math (algebra)

Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x^3−ax^2+a^2b^3x+9a^2b^2 has roots r, s, and t. Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k^2, compute the maximum possible

49. ## math

I do not undeerstand this question for homework. Determine if the set is closed for the given operation. 1. yes or no- The set of positive fractions for division. 2. yes or no=The set of positive integers for subtraction. Can someone help me? Is there a

50. ## math

Two positive integers aer in the ratio 2:5. If the product of the two integers is 40, find the larger integer.

51. ## math

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

52. ## pcm

For positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

53. ## math

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p^2)?

54. ## algebra

For a positive integer x, let f(x) be the function which returns the number of distinct positive factors of x. If p is a prime number, what is the minimum possible value of f(75p2)?

55. ## Math *URGENT

Please give the answers and solutions for each. 1.If the second term is 2 and the seventh term of a geometric sequence is 64, find the 12th term. 2. Which term if the geometric sequence 18,54,162,486,... is 3,188,646? 3. Determine the geometric mean of 8

56. ## Sigma over Phi

Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?

57. ## maths

Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?

58. ## Arithmetic Operations

Find a set of 4 distinct positive integers a,b,c,d such that the smallest positive integer that can not be represented by such expressions involving a,b,c,d (instead of 1,2,3,4) is greater than 22.You can use digits exactly once. You are allowed to reuse

59. ## MATH

Let’s agree to say that a positive integer is prime-like if it is not divisible by 2, 3, or 5. How many prime-like positive integers are there less than 100? less than 1000? A positive integer is very prime-like if it is not divisible by any prime less

60. ## math

Find the sum of the first one thousand positive integers. Explain how you arrived at your result. Now explain how to find the sum of the first n positive integers, where n is any positive integer, without adding a long list of positive integers by hand and

61. ## math

Find the sum of all positive integers m such that 2^m can be expressed as sums of four factorials (of positive integers). Details and assumptions The number n!, read as n factorial, is equal to the product of all positive integers less than or equal to n.

62. ## Math

Let a be an integer, then there are integers X, Y such that aX+(a+1)Y=1. Find the smallest positive value of Y.

The smallest possible positive value of 1−[(1/w)+(1/x)+(1/y)+(1/z)] where w, x, y, z are odd positive integers, has the form a/b, where a,b are coprime positive integers. Find a+b.

64. ## geometry

A smooth partition of the integer n is a set of positive integers a1,a2,…ak such that 1. k is a positive integer, 2. a1≤a2≤⋯≤ak, 3. ∑ki=1ai=n, and 4. ak−a1≤1. Determine how many smooth partitions there are of the integer 250.

Please check urgently .I have to submit the assignment A give an example of a function whose domain equals the set of real numbers and whose range equals the set? the set {-1,0,1} BGive an example of a function whose domain equals (0,1)and whose range

Please check urgently .I have to submit the assignment A give an example of a function whose domain equals the set of real numbers and whose range equals the set? the set {-1,0,1} BGive an example of a function whose domain equals (0,1)and whose range

67. ## MAths

4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of p/q+r/s can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?

68. ## Algebra

A positive integer minus a positive integer is always positive. This statement is sometimes true. For example, 17 – 5 = 12, but 15 – 20 = –5. post five other statements about the addition and subtraction of positive and negative integers, and ask

69. ## Math

Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b , where a and b are coprime positive integers. What is the value

70. ## algebra

Find the sum of all positive integers c such that for some prime a and a positive integer b, a^b+b^a=c^a.

71. ## pls heeelp math

For each positive integer n, let H _{n} = 1/1 +1/2 +⋯+ 1/n sum_{n=4}^{∞} 1/n*H_{n}*H_{n-1}=a/b for relatively prime positive integers a and b, find a+b

72. ## math

According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with  DAB = x, and  ABC = 90◦, andAD = BC. Say the perpendicular bisector toDC meets

73. ## Math (algebra)

Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?

74. ## math

Let Pn be the set of all subsets of the set [n]={1,2,…,n}. If two distinct elements of P5 are chosen at random, the expected number of elements (of [n]) that they have in common can be expressed as a/b where a and b are coprime positive integers. What is

75. ## Maths

Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

76. ## math

Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx

77. ## Maths

Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x3−ax2+a2b3x+9a2b2 has roots r, s, and t. Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k2, compute the maximum possible value

78. ## maths

What is the smallest positive integer with exactly 12 (positive) divisors?

79. ## math

Suppose A,B,C,D, and E are distinct positive integers such that A

80. ## math

the sum of the reciprocals of 3 consecutive positive integers is 47 divided by the product of the integers. what is the smallest of the 3 integers

81. ## algebra

Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are

82. ## math

Find the number of ordered pairs of distinct positive primes p, q (p≠q) such that p^2+7pq+q^2 is the square of an integer.

Determine the least positive integer n for which the following condition holds: No matter how the elements of the set of the first n positive integers, i.e. {1,2,…n}, are colored in red or blue, there are (not necessarily distinct) integers x,y,z, and w

84. ## maths

What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10? Details and assumptions The elements of a set are distinct, if no two of them are the same.

85. ## Math

The average of a set of five different positive integers is 360. The two smallest integers in the set are 99 and 102. What is the largest possible integer in this set?

86. ## Algebra

Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the

87. ## Math

There are three distinct ways to add four positive odd numbers to obtain 10: 1 + 1 + 3 + 5 = 10 1 + 1 + 1 + 7 = 10 1 + 3 + 3 + 3 = 10 Here, distinct means that changing the order of the numbers on the left-hand side of an equation does not count as a new

88. ## ALGEBRA!!!!

How many distinct integer values of N between 1 and 1000 are there, such that N=4a+b+4c and 2N=7a+6b+7c for some positive integers a, b and c?

89. ## Choosing Numbers That Sum to 50

What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10?

90. ## math

What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10?

91. ## Maths!!!

4 distinct integers p, q, r and s are chosen from the set {1,2,3,…,16,17}. The minimum possible value of (p/q)+(r/s) can be written as a/b, where a and b are positive, coprime integers. What is the value of a+b?

92. ## Geometry

A set of three distinct positive integers has mean 4 and median 5. What is the largest number in the set?

93. ## math

If n is a positive integer, n! is the product of the first n positive integers. For example, 4! = 4 x 3 x 2 x 1 =24. If u and v are positive integers and u!=v! x 53, then v could equal A. 6 B. 8 C. 56 D. 57

94. ## Data Structures and Algorithms

Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers

95. ## mathematics

Let 5a + 12b and 12a + 5b be the side lengths of a right-angled triangle and 13a + kb be the hypotenuse, where a, b and k are positive integers. Find the smallest possible value of k and the smallest values of a and b for that k.

96. ## math

Let 5a + 12b and 12a + 5b be the side lengths of a right-angled triangle and 13a + kb be the hypotenuse, where a, b and k are positive integers. Find the smallest possible value of k and the smallest values of a and b for that k

97. ## Mathematics

let 5a+12b and 12a+5b be the sides length of a right-angled triangle and let 13a+kb be the hypotenuse,l where a,b and k are positive integers. find the smallest possible value of k and the smallest values of a and b for that k.

98. ## math

Let 5a + 12b and 12a + 5b be the side lengths of a right-angled triangle and 13a + kb be the hypotenuse, where a, b and k are positive integers. Find the smallest possible value of k and the smallest values of a and b for that k

99. ## Mathematics

Let 5a+12b and 12a+5b be the side lengths of a right-angled triangle and 13a+kb be the hypotenuse, where a,b and k are positive integers. find the smallest possible value of k and the smallest values of a and b for that k.

100. ## MAths

Find the number of ordered pairs of distinct positive primes p, q (p≠q) such that p^2+7pq+q^2 is the square of an integer.