List questions from elementary-number-theory

Published on 15 Apr 2026 - 3:56

294

Views

How $\gcd (s,t)=1$ implies $\gcd(s-t,s+t) =1$?

Published on 16 Apr 2026 - 7:09

284

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Help prove $p^4 + 4q^4$ is never a perfect square?

Published on 15 Apr 2026 - 11:51

363

Views

A simple method of factorization $ 2^{30}+1 $

Published on 14 Apr 2026 - 0:03

2.7k

Views

$100$ consecutive natural numbers with no primes

Published on 14 Apr 2026 - 2:04

806

Views

If $2$ numbers are co-prime, does it imply that their difference is also prime to those numbers?

Published on 13 Apr 2026 - 22:05

93

Views

Are there an infinite number of primes a constant distance away from multiples of any given number?

Published on 15 Apr 2026 - 22:29

51

Views

Do elements of a Galois group act multiplicatively?

Published on 13 Apr 2026 - 23:55

191

Views

Pigeonhole principle based algorithm

Published on 10 Apr 2026 - 10:53

124

Views

Polygons inscribed in a circle and stars

Published on 16 Apr 2026 - 0:21

612

Views

A sieve for twin primes; does it imply there are infinite many twin primes?

Published on 19 Apr 2026 - 18:43

715

Views

Explain the odd/even inequality in the heights of numbers under the Collatz $(3x+1)/2$ transformation?

Published on 13 Apr 2026 - 18:11

41

Views

Pell type equation about prime

Published on 10 Apr 2026 - 17:26

136

Views

Solving a non-linear congruence for $f\in \mathbb{F}_5[x]$

Published on 15 Apr 2026 - 23:12

303

Views

Determine $2^{\frac{p-1}{4}}\equiv 1\pmod p$ or $2^{\frac{p-1}{4}}\equiv -1\pmod p$ when $p\equiv 1 \pmod 8$

Published on 17 Apr 2026 - 9:00

List Question

Why for $k$ odd, $(1+2+...+n)$ divides $(1^k+2^k+...n^k)$?

How $\gcd (s,t)=1$ implies $\gcd(s-t,s+t) =1$?

Help prove $p^4 + 4q^4$ is never a perfect square?

A simple method of factorization $ 2^{30}+1 $

$100$ consecutive natural numbers with no primes

If $2$ numbers are co-prime, does it imply that their difference is also prime to those numbers?

Are there an infinite number of primes a constant distance away from multiples of any given number?

Do elements of a Galois group act multiplicatively?

Pigeonhole principle based algorithm

Polygons inscribed in a circle and stars

A sieve for twin primes; does it imply there are infinite many twin primes?

Explain the odd/even inequality in the heights of numbers under the Collatz $(3x+1)/2$ transformation?

Pell type equation about prime

Solving a non-linear congruence for $f\in \mathbb{F}_5[x]$

Determine $2^{\frac{p-1}{4}}\equiv 1\pmod p$ or $2^{\frac{p-1}{4}}\equiv -1\pmod p$ when $p\equiv 1 \pmod 8$

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