List questions from elementary-number-theory

Published on 26 Apr 2026 - 3:26

137

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Open and closed balls in $\mathbb{Q}_p$

Published on 16 Apr 2026 - 20:43

35

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Help in proving the existence of two constants satisfying the given condition

Published on 11 Apr 2026 - 12:09

37

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$B(a, p^n) = \bar{B}(a, p^{n-1})$ in $\mathbb{Q_p}$

Published on 17 Apr 2026 - 4:19

133

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Proving that $\left\{ \frac{sm}{p} \right\} < \left\{ \frac{sn}{p} \right\} < \frac{s}{p}$ if and only if $s\not\mid p-1$

Published on 31 Mar 2026 - 2:49

216

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Only $1$ and $4900$ are squares as $1+4+9+\ldots+ n^2$

Published on 16 Apr 2026 - 6:52

1.5k

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How to prove that $g$ or $g+p$ is a primitive root modulo $p^a$ for a primitive root $g$ modulo $p$?

Published on 15 Apr 2026 - 18:39

485

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How to prove that $(\mathbb{Q},d_p)$ is not complete?

Published on 15 Apr 2026 - 13:14

59

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Combinations of divisors

Published on 10 Apr 2026 - 19:29

7.2k

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If gcd(a, b) = 1 and a | bc. Prove that a | c.

Published on 16 Apr 2026 - 13:02

906

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How to show that gcd(|a|,|b|) = gcd(a,b)?

Published on 13 Apr 2026 - 14:04

48

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Let $a$ be an odd integer. Using induction, prove: For any $n\in\mathbb{Z}^+$, $a^{2^n}\equiv 1\mod{2^{n+2}}$

Published on 15 Apr 2026 - 11:47

139

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Solving integer equation $a^3+b^3=a^2+72ab+b^2$

Published on 14 Apr 2026 - 8:39

148

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By induction showing that $m^3\le2^m$ for $m\ge10$

Published on 16 Apr 2026 - 22:31

1.2k

Views

How to solve linear congruence with two variable that is not system congruence?

Published on 08 Apr 2026 - 18:33

List Question

Is there an elementary argument for $\prod\limits_{p \le n}p < 3^n$ where $p$ is prime.

Open and closed balls in $\mathbb{Q}_p$

Help in proving the existence of two constants satisfying the given condition

$B(a, p^n) = \bar{B}(a, p^{n-1})$ in $\mathbb{Q_p}$

Proving that $\left\{ \frac{sm}{p} \right\} < \left\{ \frac{sn}{p} \right\} < \frac{s}{p}$ if and only if $s\not\mid p-1$

Only $1$ and $4900$ are squares as $1+4+9+\ldots+ n^2$

How to prove that $g$ or $g+p$ is a primitive root modulo $p^a$ for a primitive root $g$ modulo $p$?

How to prove that $(\mathbb{Q},d_p)$ is not complete?

Combinations of divisors

If gcd(a, b) = 1 and a | bc. Prove that a | c.

How to show that gcd(|a|,|b|) = gcd(a,b)?

Let $a$ be an odd integer. Using induction, prove: For any $n\in\mathbb{Z}^+$, $a^{2^n}\equiv 1\mod{2^{n+2}}$

Solving integer equation $a^3+b^3=a^2+72ab+b^2$

By induction showing that $m^3\le2^m$ for $m\ge10$

How to solve linear congruence with two variable that is not system congruence?

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