Modular Arithmetic

Welcome to the Modular Arithmetic category on Questions LLC! Here, you will find a wide range of questions and discussions related to one of the most fascinating branches of mathematics - Modular Arithmetic. Whether you are a beginner looking to understand the basics or an advanced learner seeking to explore the intricacies of this subject, you have come to the right place. Our community of experts and enthusiasts are here to provide valuable insights, solve problems, and engage in thought-provoking conversations about Modular Arithmetic. So, dive in and expand your understanding of this captivating mathematical concept.

Questions (54)

Prove that a^3 ≡ a (mod 3) for every positive integer a.What I did: Assume a^3 ≡ a (mod 3) is true for every positive
1. 4 answers
2. asked by Kid
3. 3,295 views
give an example to show that a^2 congruent to b^2 mod n need not imply that a congruent to b mod n.
1. 4 answers
2. asked by Laura
3. 1,365 views
In the statement below, the two blanks can be filled by positive single-digit numbers in such a way that the statement is always
1. 4 answers
2. asked by anonymous
3. 1,960 views
Let a = 349, M = 492186.Show that gcd(a;M) = 1. Hence find the mutliplicative inverse, a^-1 mod M
1. 4 answers
2. asked by Dean
3. 630 views
I am thinking of a number less than 60. When my number is divided by 4 it gives remainder 3 . When my number is divided by 5 it
1. 4 answers
2. asked by Jessica
3. 83 views
Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8
1. 4 answers
2. asked by john
3. 2,310 views
N is an integer such that N≡179(mod233) and N≡233(mod179).Determine a three digit positive integer M such that
1. 5 answers
2. asked by Mathslover Please help
3. 466 views
What is the remainder when 2^50 is divided by 7
1. 4 answers
2. asked by joy
3. 1,717 views
The value of x in the set{0,1,2 ...10} Satisfying 3-x≡5mod11 is.....???
1. 3 answers
2. asked by Kaur
3. 369 views
how do we find the least residue of1789 (mod 4), (mod 10), (mod 101)
1. 3 answers
2. asked by yugio
3. 1,462 views
how do we find the least residue of1789 (mod 4), (mod 10), (mod 101)
1. 3 answers
2. asked by Julie
3. 653 views
How to do modular arithmetic on TI 84?
1. 3 answers
2. asked anonymously
3. 511 views
Show that -3 is a multiplicative inverse of 17 modulo 26.
1. 2 answers
2. asked by Mat
3. 907 views
find remainders when 2^50 and 41^65 are divided by 7. this is a mod problem but I don't know how to work it...
1. 2 answers
2. asked by Laura
3. 870 views
Given $m\geq 2$ denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv
1. 2 answers
2. asked by shelly
3. 39 views
Find the multiplicative inverse of 450 modulo 359. (Express your answer as an integer n with 0 <= n < 359). You can use the fact
1. 2 answers
2. asked by becky
3. 37 views
Give an example to show that a2 ≡ b 2 (mod n) need not imply that a ≡ b(mod n)
1. 1 answer
2. asked by migbaru
3. 105 views
"Suppose that n is an odd number. Prove that n^2 is congruent to 1 modulo 8."I solved by substituting n with 1, 3, 5, and 7
1. 3 answers
2. asked by Whatismath
3. 298 views
Find the least residue of 44^8 modulo 7.
1. 1 answer
2. asked by Joann
3. 249 views
15x \equiv 20 (mod 88)13=88-5*15 2=15-1*13 1=13-2*6 GCF is 1. Im trying to use backwards substitution and so far have
1. 1 answer
2. asked by Anon
3. 406 views
So using the inverse of 17 modulo 26I have -3(y-4)(mod 26) first am I correct? (I originally started with -3(y+22)(mod 26)) And
1. 1 answer
2. asked by Anon
3. 458 views
Good morning,Just working through an example but ive gotten stuck and need some help. So find the least residue of 8^123 Mod 61
1. 4 answers
2. asked by Mat
3. 607 views
Let Z 5 be the relation of congruence modulo5.If 1 ≤ m, n ≤ 5,we define the product of two classes as [m][n] = [mn]. Explain
1. 1 answer
2. asked by Anonymous
3. 406 views
Prove that if n is an odd positive integer, then 1 ≡ n2 (mod 4).
1. 2 answers
2. asked by Don
3. 1,009 views
What are the last 2 digits of 43^2082?
1. 1 answer
2. asked by jamesbond
3. 286 views
Given $m\geq 2$, denote by $b^{-1}$ the inverse of $b\pmod{m}$. That is, $b^{-1}$ is the residue for which $bb^{-1}\equiv
1. 3 answers
2. asked by alice
3. 48 views
Prove the following theorem: Suppose p is a prime number, r, s are positive integers and x is anarbitrary integer. Then we have
1. 1 answer
2. asked by yin
3. 459 views
Use Fermat's Little Theorem to find the remainder on division 5^120 by 19.
1. 1 answer
2. asked by yin
3. 345 views
Use Fermat's Little Theorem to find the remainder on division of 5120 by 19.
1. 1 answer
2. asked by yin
3. 326 views
Prove that if n is an odd positive integer, then 1 ≡ n(power of 2) (mod 4).
1. 2 answers
2. asked by Vevea Tepou
3. 661 views
This problem from China is almost 2000 years old: Find a number that when divided by 3 gives a remainder of 2, when divided by 5
1. 2 answers
2. asked by Anonymous
3. 672 views
The canonical representative of15^11 mod3337
1. 1 answer
2. asked by Anonymous
3. 247 views
Original qustion posted here:http://www.jiskha.com/display.cgi?id=1239379999 If you do computations Modulo some number, say
1. 1 answer
2. asked by Count Iblis
3. 627 views
I would like to know if my answers are correct. I also need help solving some exercises the right way.(a) Explain why [13] is
1. 1 answer
2. asked by Jane
3. 395 views
5= (1+4)(1+4)^n= 1^n + 2*1*4 + ...+4^n which is 1 mod 4 Prove that 5^n = 1 (mod 4) for any n >or= 1.
1. 1 answer
2. asked by bobpursley
3. 396 views
Observe that the last two digits of 7^2 are 49, the last two digits of 7^3 are 43, the last two digits of 7^4 are 01, and the
1. 1 answer
2. asked by Raj
3. 453 views
Please teach me. I am completely blank with it. :(Let alpha = (3+sqrt(-3))/2 belongs to Q[sqrt(3)]. Show that if x is congruent
1. 1 answer
2. asked by student
3. 1,012 views
what is a number that divied by 3 has a remainder of 2 also that smae number divided by 4 has a remainder 3 and that same number
1. 5 answers
2. asked by Jacob
3. 1,163 views
SolveX=8(mod 11), X=9(mod 12), X=10(mod 13)
1. 2 answers
2. asked by Morris
3. 1,083 views
Consider the congruence 6x=15(mod 21). How many solutions does the congruence have? What are all the solutions?
1. 2 answers
2. asked by Shay
3. 973 views
Using 10^n = x (mod 9).Given that d=2935107 =2*10^6 + 9*10^5 + 3*10^4 + 5*10^3 + 1*10^2 + 0*10^1 + 7^10^0 Then d = kx (mod 9).
1. 2 answers
2. asked by Anonymous
3. 766 views
Let a, b, and m be integers, and m ≥ 2. Prove that:ab ≡ [ (a mod m) · (b mod m) ] (mod m). So I tried proof by cases:
1. 2 answers
2. asked by Kid
3. 663 views
Find the least positive four-digit solution to the following system of congruences.\begin{align*} 7x &\equiv 21 \pmod{14} \\
1. 3 answers
2. asked by anonymous
3. 590 views
Which two is true as i'm confusedA) 3+7 �ß 10 mod 15 17 + 9 �ß 4 mod 21 12 + 14 �ß 0 mod 26 B) 4+11 �ß 2 mod 13 9+7 �ß
1. 3 answers
2. asked by Mctagger
3. 595 views
Just a quick question:I'm trying to find the least residue of 7^5 mod 50. I've been messing about with Chinese remainder theorem
1. 3 answers
2. asked by Mrbob
3. 527 views
what is the smallest positive integer N such that 13^N \equiv 1 \pmod{2013}
1. 2 answers
2. asked by John
3. 510 views
This problem from China is almost 2000 years old: Find a number that when divided by 3 gives a remainder of 1, when divided by 5
1. 3 answers
2. asked by Christina
3. 549 views
Perform the modular arithmetic operation6.9 ( mod 5)
1. 2 answers
2. asked by nichole
3. 487 views
what does x reduce to????6x=15(mod 21) 2x=5(mod 7) x= ?(mod)7
1. 2 answers
2. asked by Shay
3. 462 views
Find the last two digits of the number 11^2016 .I need to figure out how to hand do this and show all my work. Help pls
1. 2 answers
2. asked by Anonymous
3. 466 views

Modular Arithmetic

Pages