List questions from elementary-number-theory

Published on 25 Mar 2026 - 16:02

108

Views

Show that at least two numbers that are equal among $a_1,a_2, \cdots, a_{2n}$.

Published on 01 Apr 2026 - 5:45

808

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Infinitely many integer triples $(x, y, z)$ satisfying $x^2 + 2y^2 = 3z^2$

Published on 09 Apr 2026 - 2:52

314

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The quotient of two palindromes

Published on 08 Apr 2026 - 22:25

187

Views

Finding integer solutions to $3^y = x^2 + 56$

Published on 25 Mar 2026 - 6:09

166

Views

Quantitative Aptitude Problem

Published on 10 Apr 2026 - 9:30

300

Views

A congruence involving Lucas polynomials

Published on 09 Apr 2026 - 0:04

65

Views

If $\exists n \in \mathbb{Z+}$,s.t. $2^n + 1$ is a prime, prove $\exists k \in \mathbb{Z+}, n = 2^k$

Published on 25 Mar 2026 - 7:46

1.1k

Views

Find all solutions in positive integers of the Diophantine equation $x^2+2y^2 =z^2$

Published on 14 Mar 2026 - 14:45

1.3k

Views

IMO 2017 problem #1

Published on 31 Mar 2026 - 18:18

91

Views

Measure exactly $n$ gallons of water using 9- and 15- gallon jugs...

Published on 25 Mar 2026 - 6:12

2k

Views

More than one modular multiplicative inverse possible?

Published on 25 Mar 2026 - 1:25

2.1k

Views

Hints to prove $2^{(p−1)/2}$ is congruent to 1 (mod p) or p-1 (mod p)

Published on 09 Apr 2026 - 2:00

76

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Can $n(n+x)$ with $x \leq n$ form a perfect square?

Published on 13 Mar 2026 - 17:21

87

Views

Prove an equivalence of modular-arithmetic

Published on 25 Mar 2026 - 1:36

List Question

Find all $x \in \mathbb{Z+}$ s.t. $x^2+2x-3$ is prime.

Show that at least two numbers that are equal among $a_1,a_2, \cdots, a_{2n}$.

Infinitely many integer triples $(x, y, z)$ satisfying $x^2 + 2y^2 = 3z^2$

The quotient of two palindromes

Finding integer solutions to $3^y = x^2 + 56$

Quantitative Aptitude Problem

A congruence involving Lucas polynomials

If $\exists n \in \mathbb{Z+}$,s.t. $2^n + 1$ is a prime, prove $\exists k \in \mathbb{Z+}, n = 2^k$

Find all solutions in positive integers of the Diophantine equation $x^2+2y^2 =z^2$

IMO 2017 problem #1

Measure exactly $n$ gallons of water using 9- and 15- gallon jugs...

More than one modular multiplicative inverse possible?

Hints to prove $2^{(p−1)/2}$ is congruent to 1 (mod p) or p-1 (mod p)

Can $n(n+x)$ with $x \leq n$ form a perfect square?

Prove an equivalence of modular-arithmetic

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