Question

Proving for $a>1,b > 1$, $2^a \ne p^b + 1$

score 81 · Answer 1 · 2018-08-27 20:54:46

Proving for $a>1,b > 1$, $2^a \ne p^b + 1$

Published on 27 Aug 2018 - 20:54

score 88 · Answer 2 · 2018-08-28 18:34:45

Let $p$ be prime and $n\mid p-1$. Let $gcd(a,p)=1$, and $a^{(p-1)/n} \equiv 1 \mod p$. Show that there are $n$ solutions to $x^n \equiv a \mod p$.

score 525 · Answer 3 · 2026-03-27 12:26:47

525

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A conjecture about big prime numbers

Published on 27 Mar 2026 - 12:26

score 158 · Answer 4 · 2018-08-29 09:26:00

158

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Given a prime $p = 2^n+1$, show that $\alpha^{(p-1)/2} \equiv -1 \pmod p$

Published on 29 Aug 2018 - 9:26

score 3.7k · Answer 5 · 2026-03-30 19:45:05

3.7k

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How many prime numbers in a given interval?

Published on 30 Mar 2026 - 19:45

score 77 · Answer 6 · 2018-08-29 20:04:34

77

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Could somebody prove that there are infinite values of a and b where both 6a-1 and 12b-1 are prime?

Published on 29 Aug 2018 - 20:04

score 898 · Answer 7 · 2018-08-30 00:47:31

898

Views

Question on a proof that there are infinitely many primes

Published on 30 Aug 2018 - 0:47

score 147 · Answer 8 · 2018-08-30 08:12:41

147

Views

Sumbission of answer to CMI

Published on 30 Aug 2018 - 8:12

score 1.8k · Answer 9 · 2026-03-25 13:59:05

1.8k

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Are there 3 definitions of rectangular numbers?

Published on 25 Mar 2026 - 13:59

score 151 · Answer 10 · 2018-08-30 16:07:27

151

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p is prime. Show that there is at most one $(m,n) \in \mathbb Z^2$ with $0<m\le n$ that solves $p = m^2 + n^2$

Published on 30 Aug 2018 - 16:07

score 54 · Answer 11 · 2026-03-25 04:43:44

54

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$d \in \mathbb{N}$, that is not a square, show that the continued fractions for following numbers are purely periodic

Published on 25 Mar 2026 - 4:43

score 58 · Answer 12 · 2026-03-27 14:03:29

58

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Highest power of given primen number in all binomial coefficients of n

Published on 27 Mar 2026 - 14:03

score 87 · Answer 13 · 2026-03-25 23:53:04

87

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Find when $2^{3^{4^{...^{n}}}} \equiv 1$ (mod $n+1$) is true

Published on 25 Mar 2026 - 23:53

score 582 · Answer 14 · 2026-03-30 01:52:09

582

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What is the simplest way of explaining the Riemann Hypothesis to a layman?

Published on 30 Mar 2026 - 1:52

score 102 · Answer 15 · 2026-03-25 13:55:21

102

Views

Relative prime density of $f(n)$

Published on 25 Mar 2026 - 13:55

List Question

Proving for $a>1,b > 1$, $2^a \ne p^b + 1$

Let $p$ be prime and $n\mid p-1$. Let $gcd(a,p)=1$, and $a^{(p-1)/n} \equiv 1 \mod p$. Show that there are $n$ solutions to $x^n \equiv a \mod p$.

A conjecture about big prime numbers

Given a prime $p = 2^n+1$, show that $\alpha^{(p-1)/2} \equiv -1 \pmod p$

How many prime numbers in a given interval?

Could somebody prove that there are infinite values of a and b where both 6a-1 and 12b-1 are prime?

Question on a proof that there are infinitely many primes

Sumbission of answer to CMI

Are there 3 definitions of rectangular numbers?

p is prime. Show that there is at most one $(m,n) \in \mathbb Z^2$ with $0<m\le n$ that solves $p = m^2 + n^2$

$d \in \mathbb{N}$, that is not a square, show that the continued fractions for following numbers are purely periodic

Highest power of given primen number in all binomial coefficients of n

Find when $2^{3^{4^{...^{n}}}} \equiv 1$ (mod $n+1$) is true

What is the simplest way of explaining the Riemann Hypothesis to a layman?

Relative prime density of $f(n)$

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