List questions from elementary-number-theory

Published on 16 Apr 2026 - 5:03

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Find a number such that $S(n)+P(n)=n$

Published on 15 Apr 2026 - 16:18

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Explanation of counting by Inclusion Exclusion

Published on 09 Apr 2026 - 19:09

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Let $a, b, c \gt{1}$ be integers such that $gcd(a − 1, b − 1, c − 1) \gt{1}$ Prove that $abc − 1$ is not a prime

Published on 15 Apr 2026 - 22:50

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Elementary Number Theory: Show that $3^{10}\equiv 1 \pmod{11^2}$.

Published on 16 Apr 2026 - 1:55

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there are at least $\frac{p+1}{2}$ integers $d$, with $0 \leq d < p$, so that the equation $x^3+x=d \pmod p$ has a root$\pmod p$

Published on 16 Apr 2026 - 3:39

46

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Quadratic reciprocity for some fields

Published on 15 Apr 2026 - 4:56

394

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Show that, for every integer $a$ such that $\gcd(a,100)=1$, we have $a^{20}≡1\pmod{100}$.

Published on 14 Apr 2026 - 10:20

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What is the smallest solution of $42!+k=P18\cdot P18\cdot P18\ $?

Published on 14 Apr 2026 - 19:05

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On $2xy+x+y+1 = 2ab+a+b$

Published on 15 Apr 2026 - 7:25

469

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Generalized definition of parity

Published on 14 Apr 2026 - 11:17

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Show $11^{11}+12^{12}+13^{13} =10k$ without direct calculation

Published on 12 Apr 2026 - 21:46

135

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On $xy$ vs $ab$ where $2xy+x+y+1 = 2ab+a+b$

Published on 15 Apr 2026 - 8:14

41

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Under What Conditions is $\prod_{n\in S}n^{1/n}\sim \prod_{n\in S}n^{1/|S|}$

Published on 16 Apr 2026 - 2:46

90

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Elementary Number Theory: Show the following congruence is true

Published on 15 Apr 2026 - 5:04

List Question

Why is the list $1+N,1+2N, \dots, 1+(n+1)N$ relatively prime?

Find a number such that $S(n)+P(n)=n$

Explanation of counting by Inclusion Exclusion

Let $a, b, c \gt{1}$ be integers such that $gcd(a − 1, b − 1, c − 1) \gt{1}$ Prove that $abc − 1$ is not a prime

Elementary Number Theory: Show that $3^{10}\equiv 1 \pmod{11^2}$.

there are at least $\frac{p+1}{2}$ integers $d$, with $0 \leq d < p$, so that the equation $x^3+x=d \pmod p$ has a root$\pmod p$

Quadratic reciprocity for some fields

Show that, for every integer $a$ such that $\gcd(a,100)=1$, we have $a^{20}≡1\pmod{100}$.

What is the smallest solution of $42!+k=P18\cdot P18\cdot P18\ $?

On $2xy+x+y+1 = 2ab+a+b$

Generalized definition of parity

Show $11^{11}+12^{12}+13^{13} =10k$ without direct calculation

On $xy$ vs $ab$ where $2xy+x+y+1 = 2ab+a+b$

Under What Conditions is $\prod_{n\in S}n^{1/n}\sim \prod_{n\in S}n^{1/|S|}$

Elementary Number Theory: Show the following congruence is true

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