List questions from modular-arithmetic

Published on 22 Mar 2026 - 19:50

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Show that $n^{13} - n$ is divisible by 2, 3, 5, 7, 13

Published on 31 Mar 2026 - 9:42

388

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A positive integer "modulo a sequence".

Published on 30 Mar 2026 - 6:42

129

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Prove that there are at least $4(p-3)(p-1)^{p-4}$ functions $f:S\to S$ satisfying $\sum \limits_{x\in T} x^{f(x)}\equiv a \pmod p$

Published on 28 Feb 2019 - 6:33

43

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Is it always true that $\prod_{j=1}^{w}{(2s_j + 1)} \equiv 1 \pmod 4$?

Published on 25 Mar 2026 - 17:40

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Arithmetic modulo of negative number

Published on 01 Mar 2019 - 3:25

143

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Modular arithmetic: What does $\oplus$ mean in the context of $\mathbb{Z}_n$?

Published on 01 Mar 2019 - 8:00

219

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What is the remainder when $5 000 000^{500 000 000 000}$ is divided by the prime number $10^{6}+3$?

Published on 01 Mar 2019 - 15:18

49

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Find all roots of the polynomial $f(x)=x^3-[1]_p$ in $\mathbb{Z}/1729\mathbb{Z}$

Published on 25 Mar 2026 - 15:42

1.4k

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If $p$ is congruent to 1 mod 4 where $p$ is an odd prime, then $x^2$ congruent to -1 mod $p$ has 2 solutions.

Published on 26 Mar 2026 - 12:53

99

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solving modulo equation where the mod is also a variable?

Published on 01 Mar 2019 - 19:49

909

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$m$ is prime if some integer has order $m-1$ modulo $m$

Published on 02 Mar 2019 - 2:01

113

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Chinese Remainder Theorem, when the moduli are pairwise coprime.

Published on 25 Mar 2026 - 15:46

107

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Finding $m^2, m^3, m^4, m^7, (m^3)^7$ modulo 33

Published on 03 Mar 2019 - 9:34

188

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Euler's totient function?

Published on 26 Mar 2026 - 2:52

List Question

Mathematics and the art of linearizing the circle

Show that $n^{13} - n$ is divisible by 2, 3, 5, 7, 13

A positive integer "modulo a sequence".

Prove that there are at least $4(p-3)(p-1)^{p-4}$ functions $f:S\to S$ satisfying $\sum \limits_{x\in T} x^{f(x)}\equiv a \pmod p$

Is it always true that $\prod_{j=1}^{w}{(2s_j + 1)} \equiv 1 \pmod 4$?

Arithmetic modulo of negative number

Modular arithmetic: What does $\oplus$ mean in the context of $\mathbb{Z}_n$?

What is the remainder when $5 000 000^{500 000 000 000}$ is divided by the prime number $10^{6}+3$?

Find all roots of the polynomial $f(x)=x^3-[1]_p$ in $\mathbb{Z}/1729\mathbb{Z}$

If $p$ is congruent to 1 mod 4 where $p$ is an odd prime, then $x^2$ congruent to -1 mod $p$ has 2 solutions.

solving modulo equation where the mod is also a variable?

$m$ is prime if some integer has order $m-1$ modulo $m$

Chinese Remainder Theorem, when the moduli are pairwise coprime.

Finding $m^2, m^3, m^4, m^7, (m^3)^7$ modulo 33

Euler's totient function?

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