List questions from fermat-numbers

Published on 01 Oct 2020 - 3:07

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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 06 Nov 2020 - 23:28

100

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Fermat numbers question

Published on 24 Nov 2020 - 18:07

45

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Fermat numbers question.

Published on 27 Nov 2020 - 17:46

95

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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 29 Nov 2020 - 22:30

684

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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 09 Jan 2021 - 14:46

86

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modular arthmetic

Published on 19 Jan 2021 - 14:55

381

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In regards to the Beal's conjecture

Published on 27 Jan 2021 - 3:50

124

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Fermat number proof

Published on 25 Apr 2021 - 13:20

51

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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 22 Jun 2021 - 6:15

107

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

Published on 27 Jul 2021 - 16:39

179

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

Published on 13 Aug 2021 - 12:44

246

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

Published on 01 Nov 2021 - 5:32

75

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

Published on 06 Dec 2021 - 21:49

66

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

Published on 18 Feb 2022 - 7:18

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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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