The numbers from $11111$ to $99999$ are written in a random order, one after another, forming a single number. Prove that it cannot be a power of $2$.

score 35 · Answer 7 · 2026-04-14 20:20:45

35

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Congruence equation $v^q \equiv a \pmod p $

Published on 14 Apr 2026 - 20:20

score 51 · Answer 8 · 2026-04-14 07:32:51

51

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Specific Prime Numbers Chain proofs of maximum length limits.

Published on 14 Apr 2026 - 7:32

score 836 · Answer 9 · 2026-04-14 09:36:13

836

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Is there any perfect power in the sequence $12,123,1234,12345,...$?

Published on 14 Apr 2026 - 9:36

score 70 · Answer 10 · 2026-04-15 12:42:51

70

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Let $n \in \mathbb{Z}$. Prove $n^6 = k^9 = m^4$ and Let $a = n^6$ $\iff$ $a$ must be a perfect $36$-th power.

Published on 15 Apr 2026 - 12:42

score 271 · Answer 11 · 2026-04-09 19:38:35

271

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Can $(5^k+1)(2^k)$ be a perfect power?

Published on 09 Apr 2026 - 19:38

score 225 · Answer 12 · 2026-04-17 14:16:47

225

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Is $7$ the largest possible value of $n$ for which $(1!+2!+3!+…n!)+16$ is a perfect power?

Published on 17 Apr 2026 - 14:16

score 150 · Answer 13 · 2026-04-13 10:45:51

150

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For which $x,n$ is the finite geometric series a perfect power?

Published on 13 Apr 2026 - 10:45

score 196 · Answer 14 · 2026-04-15 20:30:10

196

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Is $S_n=1!^{1!}+2!^{2!}+3!^{3!}+\cdots+n!^{n!}$ a perfect power if $n\geq2$

Published on 15 Apr 2026 - 20:30

score 73 · Answer 15 · 2026-05-11 04:10:38

73

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Is $1105$ the only Poulet-number of the form $2^a+3^b$?

Published on 11 May 2026 - 4:10

List Question

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The numbers from $11111$ to $99999$ are written in a random order, one after another, forming a single number. Prove that it cannot be a power of $2$.

Congruence equation $v^q \equiv a \pmod p $

Specific Prime Numbers Chain proofs of maximum length limits.

Is there any perfect power in the sequence $12,123,1234,12345,...$?

Let $n \in \mathbb{Z}$. Prove $n^6 = k^9 = m^4$ and Let $a = n^6$ $\iff$ $a$ must be a perfect $36$-th power.

Can $(5^k+1)(2^k)$ be a perfect power?

Is $7$ the largest possible value of $n$ for which $(1!+2!+3!+…n!)+16$ is a perfect power?

For which $x,n$ is the finite geometric series a perfect power?

Is $S_n=1!^{1!}+2!^{2!}+3!^{3!}+\cdots+n!^{n!}$ a perfect power if $n\geq2$

Is $1105$ the only Poulet-number of the form $2^a+3^b$?

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