List questions from number-theory

Published on 13 Apr 2026 - 7:40

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More precise version of Mertens theorem

Published on 14 Apr 2026 - 4:10

1.4k

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Primes of the form $x^2+ny^2$?

Published on 14 May 2026 - 9:59

92

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Integer, when reversing its digits, it doubles

Published on 10 Apr 2026 - 22:47

84

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Integer Factoring - Check if $N=a^{b}$ for some integers $a$ and $b$

Published on 15 Apr 2026 - 21:07

147

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$2n = \phi(a) + \phi(b)$

Published on 10 May 2026 - 14:03

1.4k

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Find all solutions to the system $x \equiv 1 \pmod 4, x \equiv 0 \pmod 3$, and $x \equiv 5 \pmod 7$

Published on 10 May 2026 - 17:17

139

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Finding all functions $ f : \mathbb N^\to\mathbb N^$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $

Published on 16 Apr 2026 - 10:55

3k

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find all integers $n$ such that $2^{n-1}*n+1$ is a perfect square.

Published on 14 May 2026 - 9:57

46

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if a polynomial $P(x)\in \mathbb {Z} [x]$ is a power of $n$ for all integer values of x, then $P(x)$ is the $n$th power of a polynomial?

Published on 14 Apr 2026 - 4:24

243

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Is Riemann's R-function $R(x)$ differentiable?

Published on 14 May 2026 - 20:52

175

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Prove that $10|n+3n^3+7n^7+9n^9$

Published on 14 May 2026 - 9:58

119

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Expected number of digits of the smallest prime factor of $77^{77}-18$

Published on 13 Apr 2026 - 22:13

101

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From infinite product to infinite sum and a needed expression

Published on 12 Apr 2026 - 12:52

128

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Showing that $2^{2^{2^x}}<100^{100^x}$ for large $x$

Published on 15 Apr 2026 - 9:11

List Question

How many integers $a,b,c$, both positive and negative, such that $P=a^b b^c c^a$ is a prime number?

More precise version of Mertens theorem

Primes of the form $x^2+ny^2$?

Integer, when reversing its digits, it doubles

Integer Factoring - Check if $N=a^{b}$ for some integers $a$ and $b$

$2n = \phi(a) + \phi(b)$

Find all solutions to the system $x \equiv 1 \pmod 4, x \equiv 0 \pmod 3$, and $x \equiv 5 \pmod 7$

Finding all functions $ f : \mathbb N^\to\mathbb N^$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $

find all integers $n$ such that $2^{n-1}*n+1$ is a perfect square.

if a polynomial $P(x)\in \mathbb {Z} [x]$ is a power of $n$ for all integer values of x, then $P(x)$ is the $n$th power of a polynomial?

Is Riemann's R-function $R(x)$ differentiable?

Prove that $10|n+3n^3+7n^7+9n^9$

Expected number of digits of the smallest prime factor of $77^{77}-18$

From infinite product to infinite sum and a needed expression

Showing that $2^{2^{2^x}}<100^{100^x}$ for large $x$

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