List questions from elementary-number-theory

Published on 14 Apr 2026 - 17:39

132

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Prove that there are at least $4(p-3)(p-1)^{p-4}$ functions $f:S\to S$ satisfying $\sum \limits_{x\in T} x^{f(x)}\equiv a \pmod p$

Published on 16 Apr 2026 - 16:17

974

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Find some digits of $17!$

Published on 14 Apr 2026 - 5:23

73

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$(a,b) = 1$ iff whenever $p$ is prime and $p \vert a$, then $p \nmid b$

Published on 06 May 2026 - 6:39

1.9k

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Is there any other number that has similar properties as $21$?

Published on 16 Apr 2026 - 16:56

657

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Determine all positive integer solutions for $\frac 1x + \frac 1y + \frac 1z + \frac 1{xy} + \frac1{yz} + \frac 1{xz} + \frac 1{xyz} = 1$

Published on 16 Apr 2026 - 18:48

114

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Proving $3\mid p^3 \implies 3\mid p$

Published on 15 Apr 2026 - 16:38

733

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Number of ways of representing a number as the sum of four squares

Published on 13 Apr 2026 - 3:00

219

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Paper folding and continued fractions

Published on 10 Apr 2026 - 4:46

50

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Find all roots of the polynomial $f(x)=x^3-[1]_p$ in $\mathbb{Z}/1729\mathbb{Z}$

Published on 14 Apr 2026 - 18:04

91

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Best comprehensive guide to number terminology

Published on 12 Apr 2026 - 11:55

68

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Is this property of LCM provable?

Published on 14 Apr 2026 - 1:33

40

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number of solutions of $ x^2$ $\equiv$ $-1$ mod $2^k$

Published on 15 Apr 2026 - 11:12

1k

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What is the name of rule: $a^2\cdot b^2 = (ab)^2$ and how to justify it mathematically?

Published on 14 Apr 2026 - 12:25

410

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Inequalities involving the greatest common divisor

Published on 10 May 2026 - 16:32

List Question

Diophantine equation: $x^2 - xy + ay^2 = b$

Prove that there are at least $4(p-3)(p-1)^{p-4}$ functions $f:S\to S$ satisfying $\sum \limits_{x\in T} x^{f(x)}\equiv a \pmod p$

Find some digits of $17!$

$(a,b) = 1$ iff whenever $p$ is prime and $p \vert a$, then $p \nmid b$

Is there any other number that has similar properties as $21$?

Determine all positive integer solutions for $\frac 1x + \frac 1y + \frac 1z + \frac 1{xy} + \frac1{yz} + \frac 1{xz} + \frac 1{xyz} = 1$

Proving $3\mid p^3 \implies 3\mid p$

Number of ways of representing a number as the sum of four squares

Paper folding and continued fractions

Find all roots of the polynomial $f(x)=x^3-[1]_p$ in $\mathbb{Z}/1729\mathbb{Z}$

Best comprehensive guide to number terminology

Is this property of LCM provable?

number of solutions of $ x^2$ $\equiv$ $-1$ mod $2^k$

What is the name of rule: $a^2\cdot b^2 = (ab)^2$ and how to justify it mathematically?

Inequalities involving the greatest common divisor

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