List questions from modular-arithmetic

Published on 25 Mar 2026 - 8:05

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If a ≡ b (mod n) and m|n, then a ≡ b (mod m)

Published on 25 Mar 2026 - 8:08

117

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If 13 does not divide m, then prove that $m^4+8$ is not a cube of an integer

Published on 10 May 2026 - 15:02

3.6k

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Prove that $2^{5n + 1} + 5^{n + 2} $ is divisible by 27 for any positive integer

Published on 10 May 2026 - 16:11

85

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Can at most $3$ distinct primes divide $n^3-n$, for infinitely many $n$?

Published on 10 May 2026 - 15:02

87

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Solve $x^3+3x^2-6x-88\equiv0\bmod{402}$

Published on 10 May 2026 - 14:05

23

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How can I prove that $L_{[a]}$ is not injective?

Published on 08 Apr 2026 - 18:19

96

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Find remainder of $29^{282239}$ mod $68600$

Published on 25 Mar 2026 - 8:09

106

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For prime numbers $p_n$ it holds $m\equiv p_n^2\pmod {p_{n+1}}\implies$ $m$ is a square

Published on 10 May 2026 - 11:42

282

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20 digit number game, where the only the digits 1, 2, 3, 4, 5 are allowed.

Published on 26 Mar 2026 - 9:19

515

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What is $\underbrace{2018^{2018^{2018^{\mathstrut^{.^{.^{.^{2018}}}}}}}}_{p\,\text{times}}\pmod p$ where $p$ is an odd prime?

Published on 02 May 2026 - 18:32

56

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Find all solutions for $3x+y \equiv 2 \pmod{9}$

Published on 10 May 2026 - 14:05

84

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Solutions to $x^4+x^3-x-1\equiv0\bmod15$

Published on 15 Apr 2026 - 22:16

173

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Powers of $2$ in multiplicative groups of odd composite modulus

Published on 11 Apr 2026 - 10:04

58

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When is $(p^2-1)/8$ even?

Published on 10 May 2026 - 9:27

List Question

Congruence equation doubt

If a ≡ b (mod n) and m|n, then a ≡ b (mod m)

If 13 does not divide m, then prove that $m^4+8$ is not a cube of an integer

Prove that $2^{5n + 1} + 5^{n + 2} $ is divisible by 27 for any positive integer

Can at most $3$ distinct primes divide $n^3-n$, for infinitely many $n$?

Solve $x^3+3x^2-6x-88\equiv0\bmod{402}$

How can I prove that $L_{[a]}$ is not injective?

Find remainder of $29^{282239}$ mod $68600$

For prime numbers $p_n$ it holds $m\equiv p_n^2\pmod {p_{n+1}}\implies$ $m$ is a square

20 digit number game, where the only the digits 1, 2, 3, 4, 5 are allowed.

What is $\underbrace{2018^{2018^{2018^{\mathstrut^{.^{.^{.^{2018}}}}}}}}_{p\,\text{times}}\pmod p$ where $p$ is an odd prime?

Find all solutions for $3x+y \equiv 2 \pmod{9}$

Solutions to $x^4+x^3-x-1\equiv0\bmod15$

Powers of $2$ in multiplicative groups of odd composite modulus

When is $(p^2-1)/8$ even?

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