List questions from perfect-powers

Published on 11 Apr 2026 - 16:10

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How many perfect powers are there amoung the first 1000 positive integers

Published on 12 Apr 2026 - 23:12

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Finding values to make an equation with a $x^4$ into a perfect square

Published on 12 Apr 2026 - 3:03

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What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

Published on 14 Apr 2026 - 22:18

268

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Quick! Prove that $3^{15}+37$ is a square.

Published on 16 Apr 2026 - 20:56

138

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Are there infinite many perfect powers consisting of at most two decimal digits?

Published on 10 Apr 2026 - 19:13

213

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How sure can we be that $\underbrace {k\cdots k}_{m\ k's}$ cannot be a perfect power?

Published on 13 Apr 2026 - 22:02

48

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There is no $a, b, n \in N, b \ge 2 $ such $a^{b} = 2017^{n} +43$

Published on 14 Apr 2026 - 23:37

395

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Find all positive integers $a, b, c$ such that $21^a+ 28^b= 35^c$ .

Published on 10 May 2026 - 15:46

551

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$n$-th term of the series 1 27 125 1000

Published on 16 Apr 2026 - 4:12

293

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Riemann Zeta function, perfect powers, and the Mobius function

Published on 10 May 2026 - 15:21

219

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When does the recurrence $a_k = 3a_{k - 1} + 1$ reach a power of 2?

Published on 14 Apr 2026 - 13:57

597

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Counting Perfect Powers

Published on 10 May 2026 - 13:50

40

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On the number of solutions of $pq^m \equiv k\bmod{n}$

Published on 16 Apr 2026 - 13:54

2.8k

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Method to test if a number is a perfect power?

Published on 09 Apr 2026 - 19:12

List Question

What power of a number is closest to a given integer?

How many perfect powers are there amoung the first 1000 positive integers

Finding values to make an equation with a $x^4$ into a perfect square

What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

Quick! Prove that $3^{15}+37$ is a square.

Are there infinite many perfect powers consisting of at most two decimal digits?

How sure can we be that $\underbrace {k\cdots k}_{m\ k's}$ cannot be a perfect power?

There is no $a, b, n \in N, b \ge 2 $ such $a^{b} = 2017^{n} +43$

Find all positive integers $a, b, c$ such that $21^a+ 28^b= 35^c$ .

$n$-th term of the series 1 27 125 1000

Riemann Zeta function, perfect powers, and the Mobius function

When does the recurrence $a_k = 3a_{k - 1} + 1$ reach a power of 2?

Counting Perfect Powers

On the number of solutions of $pq^m \equiv k\bmod{n}$

Method to test if a number is a perfect power?

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