List questions from modular-arithmetic

Published on 22 Nov 2018 - 10:49

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How to solve system of linear congruences with the same modulo?

Published on 22 Mar 2026 - 6:08

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Prove the divisibility of $R^k_n\pm 1$ by 4

Published on 27 Mar 2026 - 1:46

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Prove that $\frac{n}{3}+\frac{n^2}{3}+\frac{n^3}{6}$ is natural number

Published on 27 Mar 2026 - 1:47

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If $a$ is of order $3$ mod a prime $p$, then ...

Published on 25 Mar 2026 - 11:54

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Prove that $1982\cdot 1983|\underbrace{22 \ldots2}_{1980}$

Published on 27 Mar 2026 - 1:46

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Solving modular exponentiation

Published on 25 Mar 2026 - 21:53

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Solve equations $x^2+x+1\equiv 0(\mod 7)$ and $2x-4\equiv 0(\mod 6)$

Published on 27 Mar 2026 - 1:46

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Show that if $p|(a^{2^n}+1)$, then $p = 2$ or $p\equiv 1 \pmod{2^{n+1}}$

Published on 25 Mar 2026 - 10:35

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modular arithmetic problem puzzle

Published on 23 Nov 2018 - 13:56

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When g and -g are both primitive roots

Published on 25 Mar 2026 - 11:53

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Elementary Number Theory: Show that $3^{10}\equiv 1 \pmod{11^2}$.

Published on 24 Nov 2018 - 20:06

391

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Show that, for every integer $a$ such that $\gcd(a,100)=1$, we have $a^{20}≡1\pmod{100}$.

Published on 25 Nov 2018 - 3:50

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Substitutions in Modular Arithmetic

Published on 25 Nov 2018 - 8:17

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Elementary Number Theory: Show the following congruence is true

Published on 25 Nov 2018 - 21:09

List Question

$c \in \mathbb{N}$, so that $c \cdot 11 = 23 \mod 103$

How to solve system of linear congruences with the same modulo?

Prove the divisibility of $R^k_n\pm 1$ by 4

Prove that $\frac{n}{3}+\frac{n^2}{3}+\frac{n^3}{6}$ is natural number

If $a$ is of order $3$ mod a prime $p$, then ...

Prove that $1982\cdot 1983|\underbrace{22 \ldots2}_{1980}$

Solving modular exponentiation

Solve equations $x^2+x+1\equiv 0(\mod 7)$ and $2x-4\equiv 0(\mod 6)$

Show that if $p|(a^{2^n}+1)$, then $p = 2$ or $p\equiv 1 \pmod{2^{n+1}}$

modular arithmetic problem puzzle

When g and -g are both primitive roots

Elementary Number Theory: Show that $3^{10}\equiv 1 \pmod{11^2}$.

Show that, for every integer $a$ such that $\gcd(a,100)=1$, we have $a^{20}≡1\pmod{100}$.

Substitutions in Modular Arithmetic

Elementary Number Theory: Show the following congruence is true

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