List questions from perfect-powers

Published on 10 Apr 2015 - 11:54

426

Views

Show that $xyxyxy$ is not a perfect power.

Published on 05 May 2015 - 4:33

275

Views

Prove the existence or the non-existence of a couple of numbers ($n$,$m$) such that $n^2=m!$

Published on 05 May 2015 - 18:59

150

Views

Solvability of the congruence $(x+a)^n\equiv x^n\pmod p$ in $x$

Published on 22 May 2015 - 19:01

1.7k

Views

Solving a little Diophantine equation:$(n-1)!+1=n^m$

Published on 07 Jun 2015 - 17:19

360

Views

Diophantine Equation $ x^n + y^n =z^n (x<y, n>2) $

Published on 08 Jun 2015 - 17:12

266

Views

If $a^b=c^d$, then $c$ and $a$ are powers of the same number?

Published on 23 Jun 2015 - 18:07

912

Views

Perfect powers of successive naturals: Can you always reach a constant difference?

Published on 30 Jun 2015 - 23:30

135

Views

Are all even numbers the difference of prime powers

Published on 03 Jul 2015 - 9:32

171

Views

Approximate a large number with perfect powers

Published on 05 Jul 2015 - 10:08

886

Views

Sums of Fourth Powers

Published on 04 Aug 2015 - 22:37

1.2k

Views

What is the relationship between number of perfect squares and number of perfect cubes?

Published on 05 Aug 2015 - 23:50

232

Views

The smallest integer whose digit sum is larger than that of its cube?

Published on 18 Aug 2015 - 13:33

476

Views

Squares of a number yields a palindrome?

Published on 25 Mar 2026 - 15:54

581

Views

Integers $n$ for which the digit sum of $n$ exceeds the digit sum of $n^5$

Published on 18 Aug 2015 - 18:58

List Question

Integer solutions to $x^{x-2}=y^{x-1}$

Show that $xyxyxy$ is not a perfect power.

Prove the existence or the non-existence of a couple of numbers ($n$,$m$) such that $n^2=m!$

Solvability of the congruence $(x+a)^n\equiv x^n\pmod p$ in $x$

Solving a little Diophantine equation:$(n-1)!+1=n^m$

Diophantine Equation $ x^n + y^n =z^n (x<y, n>2) $

If $a^b=c^d$, then $c$ and $a$ are powers of the same number?

Perfect powers of successive naturals: Can you always reach a constant difference?

Are all even numbers the difference of prime powers

Approximate a large number with perfect powers

Sums of Fourth Powers

What is the relationship between number of perfect squares and number of perfect cubes?

The smallest integer whose digit sum is larger than that of its cube?

Squares of a number yields a palindrome?

Integers $n$ for which the digit sum of $n$ exceeds the digit sum of $n^5$

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