List questions from elementary-number-theory

Published on 10 May 2026 - 20:17

81

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Can this inequality regarding odd perfect numbers be improved?

Published on 10 May 2026 - 21:20

100

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When can we factor $N$ efficiently with a representation $N^2=a^2+b^2$?

Published on 11 May 2026 - 8:23

3.5k

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Prove that $3^{2n} +7$ is divisible by 8

Published on 11 Apr 2026 - 22:23

81

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How many pairs $(x,y)$ such that $x+2=y$ have an $x$ or $y$ divisible by 5 and not 3?

Published on 15 Apr 2026 - 22:08

418

Views

monochromatic solution to $xy=z$

Published on 10 May 2026 - 16:18

249

Views

Integer solutions to cubic equation

Published on 11 May 2026 - 9:26

476

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Longest sequence of consecutive integers which are not coprime with $n!$

Published on 13 Apr 2026 - 8:34

97

Views

An analogue to Euler's sum of powers conjecture

Published on 12 Apr 2026 - 6:51

182

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Odd numbers with $\varphi(n)/n < 1/2$

Published on 11 May 2026 - 8:24

106

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y divides discriminant implies y^2 divides it

Published on 12 Apr 2026 - 23:11

105

Views

sum of squares of digits of number n

Published on 13 Apr 2026 - 12:52

311

Views

What is the maximum value of $(a+ b+c)$ if $(a^n + b^n + c^n)$ is divisible by $(a+ b+c)$ where the remainder is 0?

Published on 14 Apr 2026 - 4:55

216

Views

Is this a valid conclusion from Chebyshev's first and second function

Published on 15 May 2026 - 17:29

93

Views

Determine when $\frac{n!-1}{3n+1}$ is an integer

Published on 10 Apr 2026 - 21:22

List Question

On some inequalities relating the special/Euler prime and non-Euler part of odd perfect numbers

Can this inequality regarding odd perfect numbers be improved?

When can we factor $N$ efficiently with a representation $N^2=a^2+b^2$?

Prove that $3^{2n} +7$ is divisible by 8

How many pairs $(x,y)$ such that $x+2=y$ have an $x$ or $y$ divisible by 5 and not 3?

monochromatic solution to $xy=z$

Integer solutions to cubic equation

Longest sequence of consecutive integers which are not coprime with $n!$

An analogue to Euler's sum of powers conjecture

Odd numbers with $\varphi(n)/n < 1/2$

y divides discriminant implies y^2 divides it

sum of squares of digits of number n

What is the maximum value of $(a+ b+c)$ if $(a^n + b^n + c^n)$ is divisible by $(a+ b+c)$ where the remainder is 0?

Is this a valid conclusion from Chebyshev's first and second function

Determine when $\frac{n!-1}{3n+1}$ is an integer

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