Question

Prove that $\left|\left\{ 1\leq x\leq p^{2}\ :\ p^{2}\mid\left(x^{p-1}-1\right)\right\} \right|=p-1$

score 52 · Answer 1 · 2018-07-15 07:06:08

52

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Prove that $\left|\left\{ 1\leq x\leq p^{2}\ :\ p^{2}\mid\left(x^{p-1}-1\right)\right\} \right|=p-1$

Published on 15 Jul 2018 - 7:06

score 122 · Answer 2 · 2018-07-15 19:59:13

122

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Prime Number Theorem Related functions Divisibility Relation Counter Sought

Published on 15 Jul 2018 - 19:59

score 221 · Answer 3 · 2026-03-26 00:11:59

221

Views

Nontrivial integer solutions of $ a^3+b^3=c^3+d^3$

Published on 26 Mar 2026 - 0:11

score 41 · Answer 4 · 2026-03-25 17:40:35

41

Views

Factorization of $(q^q - (-1)^{(q-1)/2})/(q-(-1)^{(q-1)/2})$

Published on 25 Mar 2026 - 17:40

score 454 · Answer 5 · 2018-07-16 09:28:06

454

Views

Algorithm to find prime numbers

Published on 16 Jul 2018 - 9:28

score 140 · Answer 6 · 2026-03-26 14:21:16

140

Views

Show divergence of an infinite product with terms containing congruence-restricted primes

Published on 26 Mar 2026 - 14:21

score 1.6k · Answer 7 · 2018-07-16 20:20:34

1.6k

Views

Is there an intuitive reason why the natural logarithm shows up in the Prime Number Theorem?

Published on 16 Jul 2018 - 20:20

score 444 · Answer 8 · 2026-03-27 02:37:22

444

Views

Nontrivial integer solutions of $ a^3+b^3=c^3+d^3$ and $a+b=c+d$

Published on 27 Mar 2026 - 2:37

score 204 · Answer 9 · 2026-03-27 01:00:10

204

Views

Nontrivial integer solutions of $\sum_{i=1}^3 a_i ^3=\sum_{i=1}^3 b_i ^3$ and $\sum_{i=1}^3 a_i =\sum_{i=1}^3 b_i$

Published on 27 Mar 2026 - 1:00

score 261 · Answer 10 · 2026-03-25 19:11:40

261

Views

How were the factors of $\frac{521^{521}-1}{520}$ found?

Published on 25 Mar 2026 - 19:11

score 2.5k · Answer 11 · 2018-07-17 18:34:23

2.5k

Views

The square of a prime is one greater than a multiple of 24?

Published on 17 Jul 2018 - 18:34

score 149 · Answer 12 · 2018-07-17 18:45:34

149

Views

For prime $p$ do we have $p^3+p^2+p+1=n^2$ infinitely often?

Published on 17 Jul 2018 - 18:45

score 1.8k · Answer 13 · 2026-03-26 08:02:18

1.8k

Views

How to prove that all primes of the form $4k+1$ can be represented by the sum of two squares in only one way regardless of the order?

Published on 26 Mar 2026 - 8:02

score 48 · Answer 14 · 2026-03-27 02:37:22

48

Views

Help in understanding arithmetic form of Euler's proof of infinite primes.

Published on 27 Mar 2026 - 2:37

score 374 · Answer 15 · 2018-07-19 13:36:46

374

Views

Prove that there is no positive integer $n$ such that $1^{2000} + 2^{2000} + \ldots + n^{2000}$ is prime.

Published on 19 Jul 2018 - 13:36

List Question

Prove that $\left|\left\{ 1\leq x\leq p^{2}\ :\ p^{2}\mid\left(x^{p-1}-1\right)\right\} \right|=p-1$

Prime Number Theorem Related functions Divisibility Relation Counter Sought

Nontrivial integer solutions of $ a^3+b^3=c^3+d^3$

Factorization of $(q^q - (-1)^{(q-1)/2})/(q-(-1)^{(q-1)/2})$

Algorithm to find prime numbers

Show divergence of an infinite product with terms containing congruence-restricted primes

Is there an intuitive reason why the natural logarithm shows up in the Prime Number Theorem?

Nontrivial integer solutions of $ a^3+b^3=c^3+d^3$ and $a+b=c+d$

Nontrivial integer solutions of $\sum_{i=1}^3 a_i ^3=\sum_{i=1}^3 b_i ^3$ and $\sum_{i=1}^3 a_i =\sum_{i=1}^3 b_i$

How were the factors of $\frac{521^{521}-1}{520}$ found?

The square of a prime is one greater than a multiple of 24?

For prime $p$ do we have $p^3+p^2+p+1=n^2$ infinitely often?

How to prove that all primes of the form $4k+1$ can be represented by the sum of two squares in only one way regardless of the order?

Help in understanding arithmetic form of Euler's proof of infinite primes.

Prove that there is no positive integer $n$ such that $1^{2000} + 2^{2000} + \ldots + n^{2000}$ is prime.

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