List questions from elementary-number-theory

Published on 19 Feb 2018 - 23:06

252

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Hard Imo Question

Published on 11 Apr 2026 - 1:40

884

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Prove that $76$ raised to any integer power and then divided by $100$ (ignoring the remainder) is always divisible by $57$

Published on 25 Mar 2026 - 3:21

106

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$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Published on 26 Mar 2026 - 8:02

97

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Is $7+13k$ ever a perfect square (for $k$ in $Z$)? (Part of a question regarding modulus)

Published on 12 Apr 2026 - 8:44

72

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Bound a natural by two consecutive powers

Published on 09 Apr 2026 - 3:36

70

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Find all $x \in \mathbb Z_{360}$ such that $x^2 ≡ 0 \pmod{360}$

Published on 24 Mar 2026 - 23:44

357

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Binomial coefficient: Search for multiples of 13

Published on 25 Mar 2026 - 7:54

188

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Solving $x^{17}=17$ modulo 23

Published on 21 Feb 2018 - 5:56

72

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No positive integers $a,b$ exist such that $7ab = 17(a+b)$

Published on 21 Feb 2018 - 7:43

73

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Question on notation of $\mathbb{F}[t]$

Published on 01 Apr 2026 - 14:50

166

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How to show that for each $n\in\mathbb{N}$, $\gcd(3^{n}+5^{n+1},3^{n+1}+5^{n})=2$ or $ 14$?

Published on 25 Mar 2026 - 7:46

123

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$\forall n \in \mathbb{N}$. $p(n)$ is prime?

Published on 21 Feb 2018 - 11:38

186

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Show $\lim_{n\to \infty}{|A_{n}|+|A_{n-2}| \above 1.5pt |A_{n-1}|}=2$

Published on 25 Mar 2026 - 5:41

190

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Closure on a Superset of the Rationals

Published on 12 Apr 2026 - 2:12

List Question

Is it true that $76^n=76\pmod{100}$ for all $n>0$?

Hard Imo Question

Prove that $76$ raised to any integer power and then divided by $100$ (ignoring the remainder) is always divisible by $57$

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Is $7+13k$ ever a perfect square (for $k$ in $Z$)? (Part of a question regarding modulus)

Bound a natural by two consecutive powers

Find all $x \in \mathbb Z_{360}$ such that $x^2 ≡ 0 \pmod{360}$

Binomial coefficient: Search for multiples of 13

Solving $x^{17}=17$ modulo 23

No positive integers $a,b$ exist such that $7ab = 17(a+b)$

Question on notation of $\mathbb{F}[t]$

How to show that for each $n\in\mathbb{N}$, $\gcd(3^{n}+5^{n+1},3^{n+1}+5^{n})=2$ or $ 14$?

$\forall n \in \mathbb{N}$. $p(n)$ is prime?

Show $\lim_{n\to \infty}{|A_{n}|+|A_{n-2}| \above 1.5pt |A_{n-1}|}=2$

Closure on a Superset of the Rationals

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