List questions from elementary-number-theory

Published on 11 Apr 2026 - 20:47

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Proof that if $n^2-1$ is divisible by $8$ then $n$ is odd

Published on 14 Apr 2026 - 2:21

818

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Finding the values of $x$ such that $[x^2]=[x]^2$ ($[\cdot]$ denotes the floor function)

Published on 16 Apr 2026 - 4:45

218

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Rational number and irrational number

Published on 17 Apr 2026 - 4:37

757

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Proving $10240...02401$ composite

Published on 14 Apr 2026 - 19:47

162

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Find an integer $a$ such that $(x-a)(x-10)+1=(x-b)(x-c)$ for some integers $b$ and $c$

Published on 15 Apr 2026 - 21:59

71

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How to evaluate $ \prod_{1\le i <j\le\frac{p-1}{2}}j^2-i^2 \pmod p$

Published on 14 Apr 2026 - 7:26

855

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For all integers $n$: if $7n+4$ is even, then $5n+6$ is even.

Published on 15 Apr 2026 - 10:17

75

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Polynomial problem with unknown coefficients $a, b, c$

Published on 12 Apr 2026 - 12:18

1.7k

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If $n$ is an integer and $3n+2$ is even, then $n$ is even.

Published on 15 Apr 2026 - 6:16

258

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If $m$ is a divisor of $k$ and $n$ is a divisor of $k$ and $m$ and $n$ prime to each other then $mn$ is divisor of $k$.

Published on 16 Apr 2026 - 15:54

858

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How to prove the generalized associative law for addition on $\mathbb N$?

Published on 12 Apr 2026 - 18:33

462

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Reference Request for solution of Ramanujan Identities

Published on 14 Apr 2026 - 15:40

145

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Minkowski bound of $229$-th cyclotomic field

Published on 15 Apr 2026 - 4:05

104

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Odd amicable pairs

Published on 13 Apr 2026 - 18:53

List Question

Generalized Pythagorean integer solutions

Proof that if $n^2-1$ is divisible by $8$ then $n$ is odd

Finding the values of $x$ such that $[x^2]=[x]^2$ ($[\cdot]$ denotes the floor function)

Rational number and irrational number

Proving $10240...02401$ composite

Find an integer $a$ such that $(x-a)(x-10)+1=(x-b)(x-c)$ for some integers $b$ and $c$

How to evaluate $ \prod_{1\le i <j\le\frac{p-1}{2}}j^2-i^2 \pmod p$

For all integers $n$: if $7n+4$ is even, then $5n+6$ is even.

Polynomial problem with unknown coefficients $a, b, c$

If $n$ is an integer and $3n+2$ is even, then $n$ is even.

If $m$ is a divisor of $k$ and $n$ is a divisor of $k$ and $m$ and $n$ prime to each other then $mn$ is divisor of $k$.

How to prove the generalized associative law for addition on $\mathbb N$?

Reference Request for solution of Ramanujan Identities

Minkowski bound of $229$-th cyclotomic field

Odd amicable pairs

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