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 32 · Answer 7 · 2023-06-29 03:28:03

32

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

Published on 29 Jun 2023 - 3:28

score 48 · Answer 8 · 2023-07-09 02:07:52

48

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Specific Prime Numbers Chain proofs of maximum length limits.

Published on 09 Jul 2023 - 2:07

score 833 · Answer 9 · 2023-07-14 03:36:55

833

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

Published on 14 Jul 2023 - 3:36

score 67 · Answer 10 · 2023-07-20 11:28:41

67

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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 20 Jul 2023 - 11:28

score 268 · Answer 11 · 2023-07-30 11:12:10

268

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

Published on 30 Jul 2023 - 11:12

score 220 · Answer 12 · 2023-08-04 19:27:07

220

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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 04 Aug 2023 - 19:27

score 147 · Answer 13 · 2023-08-14 15:22:00

147

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

Published on 14 Aug 2023 - 15:22

score 193 · Answer 14 · 2023-08-16 00:11:22

193

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

Published on 16 Aug 2023 - 0:11

score 71 · Answer 15 · 2023-09-22 13:11:29

71

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

Published on 22 Sep 2023 - 13:11

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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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