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
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.

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

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.

algebra 1
Find three positive consecutive integers such that the product of the second integer and the third integer is 72.

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

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.

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

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

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

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.

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?

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

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

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]

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+n42=0 (n6)(n+7)=0 n=6 n=7 Is my work and answer correct? 7 is not a positive integer. Your first equation is

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?

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

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

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]

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?

heeeelp math
For each positive integer n, let Hn=1/1 + 1/2 +⋯+ 1/n . If ∑ (up)∞ (base)(n=4) 1/n*Hn*H(n1)= a/b for relatively prime positive integers a and b, find a+b.

Math
Find the smallest positive integer n such that sqrtxsqrt(x1)

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

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

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.

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.

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

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?

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

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?

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

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

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.

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?

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,

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

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

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

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

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

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

Number theroy
What is the 50th smallest positive integer that can be written as the sum of distinct nonnegative integer powers of 3?

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

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?

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?

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?

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

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

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

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

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)?

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)?

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)?

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)?

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

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)?

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)?

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

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

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

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.

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.

algebra!!!! please help me!!!!
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.

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.

Maths(please check urgently
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

11th grade mths
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

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?

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

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

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.

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_{n1}=a/b for relatively prime positive integers a and b, find a+b

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

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?

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

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

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

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

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

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

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

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

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.

geometry!!! please help me!!!!
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

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.

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?

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

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 lefthand side of an equation does not count as a new

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?

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?

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

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?

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

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

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

mathematics
Let 5a + 12b and 12a + 5b be the side lengths of a rightangled 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.

math
Let 5a + 12b and 12a + 5b be the side lengths of a rightangled 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

Mathematics
let 5a+12b and 12a+5b be the sides length of a rightangled 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.

math
Let 5a + 12b and 12a + 5b be the side lengths of a rightangled 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

Mathematics
Let 5a+12b and 12a+5b be the side lengths of a rightangled 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.

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.