Question

Prove that for all $n\ge2\in\mathbb{Z}$ and $p$ is prime then $n^{p^p}+p^p$ is composite.

score 128 · Answer 1 · 2026-04-14 07:52:41

128

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Prove that for all $n\ge2\in\mathbb{Z}$ and $p$ is prime then $n^{p^p}+p^p$ is composite.

Published on 14 Apr 2026 - 7:52

score 43 · Answer 2 · 2026-04-16 09:49:50

43

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solving the first 5 elements of a given recursion sequence

Published on 16 Apr 2026 - 9:49

score 400 · Answer 3 · 2026-04-17 01:29:48

400

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Find all values of $p-q$ if $p, q$ are prime and ${q+1\over q}+{p\over p+1}={2n\over n+2}$ where $n$ is a positive integer.

Published on 17 Apr 2026 - 1:29

score 87 · Answer 4 · 2026-04-13 07:22:42

87

Views

Formulating arithmetic expression to aim for target number

Published on 13 Apr 2026 - 7:22

score 436 · Answer 5 · 2026-04-14 14:24:21

436

Views

Euler's Totient Function and Residue Classes

Published on 14 Apr 2026 - 14:24

score 52 · Answer 6 · 2026-05-13 11:53:44

52

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Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

Published on 13 May 2026 - 11:53

score 82 · Answer 7 · 2026-04-12 03:07:30

82

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A question about integer BMO 1984 Question 4

Published on 12 Apr 2026 - 3:07

score 520 · Answer 8 · 2026-04-20 00:43:57

520

Views

Number of pairs $(a,b)$ such that $\;gcd(a,b)=x \quad (1\leq a,b\leq N)$

Published on 20 Apr 2026 - 0:43

score 70 · Answer 9 · 2026-04-15 08:09:04

70

Views

Show that $2018^{6k+2}$ can't be written as $a^3+b^3+c^3$, where $a,b,c\in \mathbb {N} $.

Published on 15 Apr 2026 - 8:09

score 105 · Answer 10 · 2026-04-15 23:06:11

105

Views

Showing that $x^2+y^2+z^2=k^2$ has infinitely many integer solutions

Published on 15 Apr 2026 - 23:06

score 67 · Answer 11 · 2026-05-13 17:39:23

67

Views

What is the reason for taking $\omega$ to be a primitive $q$-th root unity rather than taking any $q$-th root of unity?

Published on 13 May 2026 - 17:39

score 683 · Answer 12 · 2026-04-15 20:15:02

683

Views

Prove $\gcd(m, n)=\gcd(m, 2n)$

Published on 15 Apr 2026 - 20:15

score 457 · Answer 13 · 2026-04-12 23:22:16

457

Views

How to prove that there are infinitely many primes of form $6n+1$?

Published on 12 Apr 2026 - 23:22

score 670 · Answer 14 · 2026-04-17 11:41:30

670

Views

Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.

Published on 17 Apr 2026 - 11:41

score 278 · Answer 15 · 2026-04-16 23:17:24

278

Views

Prove gcd(f(n), f(n+1))=1

Published on 16 Apr 2026 - 23:17

List Question

Prove that for all $n\ge2\in\mathbb{Z}$ and $p$ is prime then $n^{p^p}+p^p$ is composite.

solving the first 5 elements of a given recursion sequence

Find all values of $p-q$ if $p, q$ are prime and ${q+1\over q}+{p\over p+1}={2n\over n+2}$ where $n$ is a positive integer.

Formulating arithmetic expression to aim for target number

Euler's Totient Function and Residue Classes

Show that $S^p = \sum\limits_{x \in \Bbb {F_q}^*} \left ( \frac x q \right ) {\omega}^{xp}.$

A question about integer BMO 1984 Question 4

Number of pairs $(a,b)$ such that $\;gcd(a,b)=x \quad (1\leq a,b\leq N)$

Show that $2018^{6k+2}$ can't be written as $a^3+b^3+c^3$, where $a,b,c\in \mathbb {N} $.

Showing that $x^2+y^2+z^2=k^2$ has infinitely many integer solutions

What is the reason for taking $\omega$ to be a primitive $q$-th root unity rather than taking any $q$-th root of unity?

Prove $\gcd(m, n)=\gcd(m, 2n)$

How to prove that there are infinitely many primes of form $6n+1$?

Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.

Prove gcd(f(n), f(n+1))=1

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