List questions from number-theory

Published on 14 Apr 2026 - 14:37

144

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$\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-...-\frac{1}{(p-1)}$=$\frac{a}{(p-1)!}$. Show that $a \equiv \frac{(2-2^p)}{p} $ (mod p)

Published on 17 Apr 2026 - 3:01

55

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Primality radii in arithmetic progression

Published on 13 Apr 2026 - 6:13

237

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When are $a+b$ and $ab$ palindromic for integers $a,b$?

Published on 07 May 2026 - 19:28

89

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Given two non-negative integer numbers $m$ and $n$ such that $m>1$ and $2^{2m+1}\ge n^2$

Published on 14 Apr 2026 - 19:45

100

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Describe set of integers $x$ such that the $p$-adic norm of $(x-a)$ is smaller than $p^{-e}$

Published on 15 Apr 2026 - 8:47

87

Views

the largest number $y$ in which $(x!)^{x+y}|(x^2)!$

Published on 13 Apr 2026 - 23:10

122

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Prime factorization of very large integer with quadratic residue and its square roots

Published on 10 May 2026 - 21:57

122

Views

A base in which all primes end with $5$ different symbols?

Published on 15 Apr 2026 - 20:07

168

Views

Perfect square or cube

Published on 14 May 2026 - 0:29

254

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Hensel´s lemma for $p$-adic numbers

Published on 14 Apr 2026 - 15:47

45

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$n$ is a positive integer, if whenever $n$ divide $ab$, $n$ also divide $a$ or a divide $b$, then n is a prime.

Published on 14 Apr 2026 - 17:56

59

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The size of $\mathbb{Z}_n *$

Published on 12 Apr 2026 - 4:22

137

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A relation concerning the "sum of squares" counting function $r_2(n)$

Published on 10 May 2026 - 13:48

98

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Is $2^\sqrt{2}$ is rational or irrational?

Published on 14 Apr 2026 - 22:48

List Question

Two sums, the relation between them

$\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-...-\frac{1}{(p-1)}$=$\frac{a}{(p-1)!}$. Show that $a \equiv \frac{(2-2^p)}{p} $ (mod p)

Primality radii in arithmetic progression

When are $a+b$ and $ab$ palindromic for integers $a,b$?

Given two non-negative integer numbers $m$ and $n$ such that $m>1$ and $2^{2m+1}\ge n^2$

Describe set of integers $x$ such that the $p$-adic norm of $(x-a)$ is smaller than $p^{-e}$

the largest number $y$ in which $(x!)^{x+y}|(x^2)!$

Prime factorization of very large integer with quadratic residue and its square roots

A base in which all primes end with $5$ different symbols?

Perfect square or cube

Hensel´s lemma for $p$-adic numbers

$n$ is a positive integer, if whenever $n$ divide $ab$, $n$ also divide $a$ or a divide $b$, then n is a prime.

The size of $\mathbb{Z}_n *$

A relation concerning the "sum of squares" counting function $r_2(n)$

Is $2^\sqrt{2}$ is rational or irrational?

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