List questions from elementary-number-theory

Published on 09 Apr 2026 - 2:06

132

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Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Published on 25 Mar 2026 - 6:28

141

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Divisibility transitive proof

Published on 10 Apr 2026 - 17:11

831

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Proof involving linear combinations and gcd of two numbers

Published on 25 Mar 2026 - 1:27

898

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p, q are be rational numbers with p < q and q ≠ 0. Prove that ${\frac{3}{p - q }}$ is rational.

Published on 21 Mar 2026 - 20:31

75

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The number of elements below $p^2$ divisible by p (p's Prime)

Published on 22 Mar 2026 - 13:19

91

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Show $\left \lfloor{x}\right \rfloor + \left \lfloor{y}\right \rfloor \leq \left \lfloor{x+y}\right \rfloor$ for every $x, y \in \mathbb{R}$

Published on 25 Mar 2026 - 9:29

114

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$\frac{(2n-1)!}{n! (n-1)!}$ is even whenever $n$ is not a power of $2$

Published on 21 Mar 2026 - 20:06

114

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Show that there's a solution to $x^2 \equiv -1 \pmod {p^2}$

Published on 09 Apr 2026 - 2:08

30

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$b\equiv a\mod pq\Leftrightarrow\ b\equiv a\mod p\text{ and }b\equiv a\mod q$

Published on 22 Mar 2026 - 12:43

109

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Two miscellaneous questions about equations involving the Euler's totient function and twin primes

Published on 09 Apr 2026 - 3:02

83

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must a primitive root be invertible?

Published on 09 Apr 2026 - 2:40

202

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Double derangement permutation

Published on 09 Apr 2026 - 5:49

55

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If$(a,b)=m$, then $(a^i,b^i)=m$

Published on 21 Mar 2026 - 18:35

153

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Sum of integers and system of equations

Published on 22 Mar 2026 - 8:39

List Question

Understanding quadratic reciprocity

Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Divisibility transitive proof

Proof involving linear combinations and gcd of two numbers

p, q are be rational numbers with p < q and q ≠ 0. Prove that ${\frac{3}{p - q }}$ is rational.

The number of elements below $p^2$ divisible by p (p's Prime)

Show $\left \lfloor{x}\right \rfloor + \left \lfloor{y}\right \rfloor \leq \left \lfloor{x+y}\right \rfloor$ for every $x, y \in \mathbb{R}$

$\frac{(2n-1)!}{n! (n-1)!}$ is even whenever $n$ is not a power of $2$

Show that there's a solution to $x^2 \equiv -1 \pmod {p^2}$

$b\equiv a\mod pq\Leftrightarrow\ b\equiv a\mod p\text{ and }b\equiv a\mod q$

Two miscellaneous questions about equations involving the Euler's totient function and twin primes

must a primitive root be invertible?

Double derangement permutation

If$(a,b)=m$, then $(a^i,b^i)=m$

Sum of integers and system of equations

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