List questions from elementary-number-theory

Published on 12 Apr 2026 - 15:27

344

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Application of Fermat's little theorem to check divisibility

Published on 09 Apr 2026 - 13:10

755

Views

$a^2 + b^2 + c^2 + d^2 + e^2=f^2$

Published on 16 Apr 2026 - 1:07

49

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Existence of $m \in M \subsetneq \mathbb{N}$ such that $p \nmid a+bm$, $p$ prime

Published on 14 Apr 2026 - 11:54

85

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How will you determine which number is bigger among $m^n$ and $n^m$ without using a calculator, $n$ and $m$ being real?

Published on 11 Apr 2026 - 20:16

610

Views

Targeting all prime numbers with a minimal set of sinusoidal functions

Published on 15 Apr 2026 - 12:31

104

Views

In $ \mathbb{Z}_p $ where $ p $ is prime, what is the number of roots of $ x^2+1\equiv 0 \mod p $?

Published on 15 Apr 2026 - 18:58

177

Views

Existence of solutions to $a^2x^2 + bx = y^2$

Published on 13 Apr 2026 - 6:04

166

Views

Show that a cube number which is also a square is of the form 7n, 7n+1

Published on 16 Apr 2026 - 2:08

286

Views

Elementary number theory in sets

Published on 15 Apr 2026 - 17:43

726

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Application of Euler's totient function to find last digits

Published on 25 Mar 2026 - 12:33

747

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Prove that $a^ n\equiv b^n\pmod{p^k}$ if and only if $n(a-b)\equiv 0 \pmod{p^k}$

Published on 16 Apr 2026 - 23:19

367

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Factorization of a $116$-digit number

Published on 13 Apr 2026 - 16:52

1.9k

Views

Let $x$, $y$ and $z$ be prime numbers. Find the number of ordered triplets such that $x^y + 1 = z$

Published on 14 Apr 2026 - 20:35

242

Views

Find $A = x - y + z$ if $3x + 5y + 7z = 29$ and $x , y , z \in \mathbb{Z}^+$

Published on 16 Apr 2026 - 10:40

List Question

Compute $\sum_{i=1}^n\frac i{\gcd(i,n)}$

Application of Fermat's little theorem to check divisibility

$a^2 + b^2 + c^2 + d^2 + e^2=f^2$

Existence of $m \in M \subsetneq \mathbb{N}$ such that $p \nmid a+bm$, $p$ prime

How will you determine which number is bigger among $m^n$ and $n^m$ without using a calculator, $n$ and $m$ being real?

Targeting all prime numbers with a minimal set of sinusoidal functions

In $ \mathbb{Z}_p $ where $ p $ is prime, what is the number of roots of $ x^2+1\equiv 0 \mod p $?

Existence of solutions to $a^2x^2 + bx = y^2$

Show that a cube number which is also a square is of the form 7n, 7n+1

Elementary number theory in sets

Application of Euler's totient function to find last digits

Prove that $a^ n\equiv b^n\pmod{p^k}$ if and only if $n(a-b)\equiv 0 \pmod{p^k}$

Factorization of a $116$-digit number

Let $x$, $y$ and $z$ be prime numbers. Find the number of ordered triplets such that $x^y + 1 = z$

Find $A = x - y + z$ if $3x + 5y + 7z = 29$ and $x , y , z \in \mathbb{Z}^+$

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