List questions from fermat-numbers

Published on 23 Feb 2026 - 12:06

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Prove the identity $\frac{1}{1+x^{1}}+\cdots+\frac{2^{n}}{1+x^{2^{n}}}=\frac{1}{x-1}+\frac{2^{n+1}}{1+x^{2^{n+1}}}$

Published on 23 Feb 2026 - 12:09

102

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Fermat numbers question

Published on 08 Apr 2026 - 16:29

46

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Fermat numbers question.

Published on 23 Feb 2026 - 11:59

96

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Number Theory: Prove for all $1\leq n \in \mathbb{N}$ $F_n \mid 2^{F_n}-2$ with $F_n$ is Fermat numbers

Published on 23 Feb 2026 - 12:09

685

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Showing that $p$ is a Fermat prime if and only if every quadratic non-residue mod $p$ is also a primitive root mod $p$

Published on 23 Feb 2026 - 12:08

89

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modular arthmetic

Published on 08 Apr 2026 - 23:40

382

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In regards to the Beal's conjecture

Published on 23 Feb 2026 - 12:04

125

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Fermat number proof

Published on 23 Feb 2026 - 11:59

52

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Showing that if $m \leq 2^n-1$, then the $m$-th Fermat number divides $2^{F_n}-2$

Published on 23 Feb 2026 - 12:08

108

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Can the substitution be different in this proof of a Fermat theorem?

Published on 23 Feb 2026 - 12:07

180

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Prove that no Fermat number is a $3$ rd power of an integer.

Published on 23 Feb 2026 - 12:07

247

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Is $3$ the only prime that is both a Mersenne prime and a Fermat prime?

Published on 23 Feb 2026 - 12:06

76

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Prove that a squared number is an equivalence relation of $-1\pmod{p}$

Published on 23 Feb 2026 - 12:06

67

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Tweaking Fermat's primality test - Why does it work and should I expect different results?

Published on 23 Feb 2026 - 12:02

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Stuck on middle step of proof that $a^{p(p-1)}=1 \pmod{p^2}$

Prove the identity $\frac{1}{1+x^{1}}+\cdots+\frac{2^{n}}{1+x^{2^{n}}}=\frac{1}{x-1}+\frac{2^{n+1}}{1+x^{2^{n+1}}}$

Fermat numbers question

Fermat numbers question.

Number Theory: Prove for all $1\leq n \in \mathbb{N}$ $F_n \mid 2^{F_n}-2$ with $F_n$ is Fermat numbers

Showing that $p$ is a Fermat prime if and only if every quadratic non-residue mod $p$ is also a primitive root mod $p$

modular arthmetic

In regards to the Beal's conjecture

Fermat number proof

Showing that if $m \leq 2^n-1$, then the $m$-th Fermat number divides $2^{F_n}-2$

Can the substitution be different in this proof of a Fermat theorem?

Prove that no Fermat number is a $3$ rd power of an integer.

Is $3$ the only prime that is both a Mersenne prime and a Fermat prime?

Prove that a squared number is an equivalence relation of $-1\pmod{p}$

Tweaking Fermat's primality test - Why does it work and should I expect different results?

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