List questions from perfect-powers

Published on 07 Jan 2017 - 14:51

303

Views

If $n^2+11$ is a prime then $n+4$ is not a cube

Published on 10 Jan 2017 - 7:44

103

Views

What values can $2^j-3^k$ have?

Published on 10 Jan 2017 - 22:16

156

Views

First decimal digit of a very large number.

Published on 19 Jan 2017 - 18:46

24

Views

Perfect square sequences starting at different offsets, how do I find intersections?

Published on 20 Feb 2017 - 2:00

57

Views

Are there arbitary large non-trivial powers NOT containing all digits?

Published on 23 Feb 2017 - 20:41

132

Views

Are there arbitary large $b$ such that the diophantine equation $a^3-n\cdot b^3=1$ has a solution?

Published on 28 Feb 2017 - 14:42

947

Views

Who can prove that a triangular number cannot be a cube, fourth power or fifth power?

Published on 13 Mar 2017 - 23:50

196

Views

Proof involving integer squares and parity

Published on 14 Mar 2017 - 2:45

73

Views

Is it known whether a triangular number can be any power with exponent greater than $2$?

Published on 14 Mar 2017 - 13:15

297

Views

Number of powers modulo prime

Published on 19 Mar 2017 - 15:27

658

Views

Can we prove that there are no two perfect powers with difference $6$?

Published on 22 Mar 2017 - 11:11

1.5k

Views

If $a^3+a^2+a=9b^3+b^2+b$ and $a,b$ are integers then show $a-b$ is a perfect cube.

Published on 01 Apr 2017 - 9:39

97

Views

Is there an easy criterion whether a number is the sum of a square and a cube?

Published on 25 Mar 2026 - 3:03

202

Views

Can $n!+16$ be a perfect square when $n\geq5$?

Published on 12 Feb 2023 - 11:06

List Question

Prove that given fraction is power of two

If $n^2+11$ is a prime then $n+4$ is not a cube

What values can $2^j-3^k$ have?

First decimal digit of a very large number.

Perfect square sequences starting at different offsets, how do I find intersections?

Are there arbitary large non-trivial powers NOT containing all digits?

Are there arbitary large $b$ such that the diophantine equation $a^3-n\cdot b^3=1$ has a solution?

Who can prove that a triangular number cannot be a cube, fourth power or fifth power?

Proof involving integer squares and parity

Is it known whether a triangular number can be any power with exponent greater than $2$?

Number of powers modulo prime

Can we prove that there are no two perfect powers with difference $6$?

If $a^3+a^2+a=9b^3+b^2+b$ and $a,b$ are integers then show $a-b$ is a perfect cube.

Is there an easy criterion whether a number is the sum of a square and a cube?

Can $n!+16$ be a perfect square when $n\geq5$?

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