List questions from elementary-number-theory

Published on 12 Apr 2026 - 20:26

34

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Equivalence class checking my answer

Published on 11 Mar 2018 - 18:55

58

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To find positive integers from $Z_8$

Published on 01 Apr 2026 - 17:18

122

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Let $e$ and $n$ be positive integers. Suppose $e$ and $φ(n)$ are relatively prime. Prove if $x^e ≡ 1\bmod(n)$, then $x ≡ 1\bmod(n)$

Published on 25 Mar 2026 - 6:22

38

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What are the possible residues

Published on 12 Apr 2026 - 15:55

114

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To find the smallest integer greater than $23$ with certain modular residues

Published on 25 Mar 2026 - 6:05

686

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Prove that in a 10-element subset of $\{1, \dots , 50 \} $ there exist 2 $5$-element subsets such that the sums of all their elements are equal.

Published on 04 Apr 2026 - 23:24

345

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If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$. Is this true or false?

Published on 09 Apr 2026 - 3:55

283

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Solving the congruence $9x \equiv 3 \pmod{47}$

Published on 25 Mar 2026 - 23:37

542

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Mathematical Induction prove that $n^3+5n$ is divisible by $6$

Published on 11 Apr 2026 - 9:47

64

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How to deal with $(-1)^{k-1}$

Published on 09 Apr 2026 - 21:45

83

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Is $1+1+(k+1)2^{k+1}<1+(k+2)2^{k+1}$, for $n=k+1$?

Published on 09 Apr 2026 - 15:58

51

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Proving $x ≡ y \pmod n $ if $x^a ≡ y^a \pmod n$

Published on 25 Mar 2026 - 22:10

1k

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Show that for prime $p\gt 3, 2p+1, 4p+1$ cannot be both prime

Published on 12 Mar 2018 - 18:03

486

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Prove that if $3\mid n$ and $5\mid n$, then $15\mid n$

Published on 25 Mar 2026 - 8:10

List Question

Linear independence "modulo $\mathbb Z^n$"

Equivalence class checking my answer

To find positive integers from $Z_8$

Let $e$ and $n$ be positive integers. Suppose $e$ and $φ(n)$ are relatively prime. Prove if $x^e ≡ 1\bmod(n)$, then $x ≡ 1\bmod(n)$

What are the possible residues

To find the smallest integer greater than $23$ with certain modular residues

Prove that in a 10-element subset of $\{1, \dots , 50 \} $ there exist 2 $5$-element subsets such that the sums of all their elements are equal.

If $5x \equiv 15 \pmod{25}$, then definitely $x \equiv 3 \pmod{25}$. Is this true or false?

Solving the congruence $9x \equiv 3 \pmod{47}$

Mathematical Induction prove that $n^3+5n$ is divisible by $6$

How to deal with $(-1)^{k-1}$

Is $1+1+(k+1)2^{k+1}<1+(k+2)2^{k+1}$, for $n=k+1$?

Proving $x ≡ y \pmod n $ if $x^a ≡ y^a \pmod n$

Show that for prime $p\gt 3, 2p+1, 4p+1$ cannot be both prime

Prove that if $3\mid n$ and $5\mid n$, then $15\mid n$

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