Question

Determine remainders of large numbers

score 112 · Answer 1 · 2026-03-29 18:32:26

112

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Determine remainders of large numbers

Published on 29 Mar 2026 - 18:32

score 33 · Answer 2 · 2019-09-27 02:35:44

33

Views

In $\Bbb{Z}/m\Bbb{Z}$, show that $([a]_m)^{qd+r} = (([a]_m)^d)^q([a]_m)^r$

Published on 27 Sep 2019 - 2:35

score 928 · Answer 3 · 2019-09-27 05:54:52

928

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Modular-arithmetic proofs

Published on 27 Sep 2019 - 5:54

score 459 · Answer 4 · 2019-09-27 07:10:14

For any integers $a$ and $b$, $ab = 0$ implies $a = 0$ or $b = 0$. Prove that this remains true mod prime numbers but not true mod a composite number.

score 240 · Answer 5 · 2026-03-29 07:39:22

240

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For what values of n is $2^{2n} -1$ divisible by $4n+1$

Published on 29 Mar 2026 - 7:39

score 49 · Answer 6 · 2026-02-23 06:35:36

49

Views

Stuck on Consecutive Moduli Selection (Residue Number System)

Published on 23 Feb 2026 - 6:35

score 97 · Answer 7 · 2019-09-27 15:52:00

97

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Given integers $m$ and $1 \lt a \lt m$, with $a \vert m$, prove that the equation $ax\equiv 1\pmod{m}$ has no solution.

Published on 27 Sep 2019 - 15:52

score 1.7k · Answer 8 · 2026-03-29 20:18:48

1.7k

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Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

Published on 29 Mar 2026 - 20:18

score 259 · Answer 9 · 2019-09-28 17:43:01

259

Views

Proof that $3^{10^n}\equiv 1\pmod{10^n},\, n\ge 2$

Published on 28 Sep 2019 - 17:43

score 315 · Answer 10 · 2019-09-29 13:03:14

315

Views

Counting primes in residue classes

Published on 29 Sep 2019 - 13:03

score 250 · Answer 11 · 2019-09-30 12:33:10

250

Views

Given two primes $p$, $q$ and their product $pq$, find $\phi(pq)$ mod $p + q$

Published on 30 Sep 2019 - 12:33

score 299 · Answer 12 · 2026-03-25 21:51:11

299

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Prove that for every natural number $n$, there is a set $S$ of $n$ natural numbers such that for any two different numbers $a,b$ From $S$ the number…

Published on 25 Mar 2026 - 21:51

score 1.1k · Answer 13 · 2026-03-26 14:42:59

1.1k

Views

Proof that if $\gcd(a,n) = 1$ then $a^k \equiv a^{k \bmod \phi(n)} \pmod {\!n}$

Published on 26 Mar 2026 - 14:42

score 56 · Answer 14 · 2026-03-30 13:40:39

56

Views

quadratic equation modulo product of coprime squarefree integers

Published on 30 Mar 2026 - 13:40

score 104 · Answer 15 · 2019-09-30 23:37:35

104

Views

Find a $k$ such that $3^k \equiv -6 \pmod{43}$

Published on 30 Sep 2019 - 23:37

List Question

Determine remainders of large numbers

In $\Bbb{Z}/m\Bbb{Z}$, show that $([a]_m)^{qd+r} = (([a]_m)^d)^q([a]_m)^r$

Modular-arithmetic proofs

For any integers $a$ and $b$, $ab = 0$ implies $a = 0$ or $b = 0$. Prove that this remains true mod prime numbers but not true mod a composite number.

For what values of n is $2^{2n} -1$ divisible by $4n+1$

Stuck on Consecutive Moduli Selection (Residue Number System)

Given integers $m$ and $1 \lt a \lt m$, with $a \vert m$, prove that the equation $ax\equiv 1\pmod{m}$ has no solution.

Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.

Proof that $3^{10^n}\equiv 1\pmod{10^n},\, n\ge 2$

Counting primes in residue classes

Given two primes $p$, $q$ and their product $pq$, find $\phi(pq)$ mod $p + q$

Prove that for every natural number $n$, there is a set $S$ of $n$ natural numbers such that for any two different numbers $a,b$ From $S$ the number…

Proof that if $\gcd(a,n) = 1$ then $a^k \equiv a^{k \bmod \phi(n)} \pmod {\!n}$

quadratic equation modulo product of coprime squarefree integers

Find a $k$ such that $3^k \equiv -6 \pmod{43}$

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