List questions from elementary-number-theory

Published on 13 Apr 2026 - 0:36

59

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On the validity of a manual-calculation-friendly variation of the Legendre's formula: $\nu_p(n!)=\sum_{i=1}^\infty\lfloor\frac{n}{p^i}\rfloor$.

Published on 16 Apr 2026 - 3:19

197

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exponentiating the natural numbers

Published on 20 Apr 2026 - 11:29

77

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Would like to get numerical (lower [and upper?]) bounds for $p$

Published on 13 Apr 2026 - 0:59

489

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Find all positive integers $x,y$ such that $\frac{x^2-1}{xy+1}$ is a non-negative integer.

Published on 15 Apr 2026 - 21:58

121

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A question about Fermat-Euler Theorem restrictions

Published on 08 Apr 2026 - 18:35

74

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Determine $\left ( \frac{5}{p} \right )=1$ in a different way

Published on 16 Apr 2026 - 6:32

35

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Given $x_o,x_1\in \mathbb{Z}$ solve $x_0^{k_0}(x_1^{k_1}(1+x_1y_1)+x_0y_0)=0$ using number theory

Published on 16 Apr 2026 - 1:39

699

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Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Published on 16 Apr 2026 - 5:42

113

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Solving $4^m-3^n=p^2$ for natural $(m,n,p)$.

Published on 16 Apr 2026 - 14:16

64

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If $d \equiv 1 \pmod 6$, then how $2^d + 1 \equiv 3 \pmod 9$?

Published on 15 Apr 2026 - 23:17

255

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If $ \ p^3q^2=r^2s^3 \ $ , then according to the fundamental theorem of arithmatic

Published on 11 Apr 2026 - 21:25

125

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Can I prove that a solution of $a^2-2b^2=p$ with $1\le b<\sqrt{p}$ always exists?

Published on 15 Apr 2026 - 15:50

106

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If a solution exists, how can I construct another solution with coprime integers?

Published on 22 Apr 2026 - 18:32

1.4k

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Euler's theorem using Lagrange's theorem?

Published on 13 Apr 2026 - 8:59

List Question

Finding the smallest n satisfying $S_n > 10$

On the validity of a manual-calculation-friendly variation of the Legendre's formula: $\nu_p(n!)=\sum_{i=1}^\infty\lfloor\frac{n}{p^i}\rfloor$.

exponentiating the natural numbers

Would like to get numerical (lower [and upper?]) bounds for $p$

Find all positive integers $x,y$ such that $\frac{x^2-1}{xy+1}$ is a non-negative integer.

A question about Fermat-Euler Theorem restrictions

Determine $\left ( \frac{5}{p} \right )=1$ in a different way

Given $x_o,x_1\in \mathbb{Z}$ solve $x_0^{k_0}(x_1^{k_1}(1+x_1y_1)+x_0y_0)=0$ using number theory

Is it true that $2^{2^{n}}$ always ends in the digit $6$?

Solving $4^m-3^n=p^2$ for natural $(m,n,p)$.

If $d \equiv 1 \pmod 6$, then how $2^d + 1 \equiv 3 \pmod 9$?

If $ \ p^3q^2=r^2s^3 \ $ , then according to the fundamental theorem of arithmatic

Can I prove that a solution of $a^2-2b^2=p$ with $1\le b<\sqrt{p}$ always exists?

If a solution exists, how can I construct another solution with coprime integers?

Euler's theorem using Lagrange's theorem?

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