List questions from fermat-numbers

Published on 24 Mar 2016 - 19:30

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Let p be a prime and k a positive integer such that $a^k$mod p = a mod p for all integers a. Prove that p - 1 divides k - 1.

Published on 06 Apr 2016 - 0:10

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Exercise fermat numbers

Published on 17 Apr 2016 - 18:56

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Let $F_n$ be a Fermat prime number prove that $\gamma_{F_n}(2)=2^{n+1}$

Published on 05 Jun 2016 - 10:44

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Why are the first 5 Fermat numbers prime?

Published on 06 Jun 2016 - 23:53

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Proving a property of about the Fermat numbers

Published on 29 Jan 2014 - 5:21

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What is the connection between Fermat's Little Theorem and "Fermat Liars"?

Published on 12 Apr 2017 - 0:39

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Prove there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.

Published on 14 Apr 2017 - 22:52

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Modular Congruence of the Fermat Numbers

Published on 17 Apr 2017 - 13:24

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Non prime modulus of prime powers

Published on 26 Apr 2017 - 14:53

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Euler Totient of Fermat Numbers

Published on 10 May 2017 - 1:55

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primality of $\frac{(2^{19}+1)}{3}$ and $\frac{(2^{23}+1)}{3}$

Published on 30 Jun 2017 - 12:53

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Induction on Fermat Numbers: $F_n = \prod_{j=0}^{n-1}F_j+2$

Published on 09 Aug 2017 - 0:31

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$2^n + 1$ is prime $ \implies n$ is a power of $2$

Published on 15 Aug 2017 - 4:15

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If $F_m = 2^{2^m} + 1$ is prime (with $m \geq 1$), does it follow that $3 \mid \frac{F_m + 1}{2}$?

Published on 10 Sep 2017 - 15:20

List Question

Sum of Two Squares product primality

Let p be a prime and k a positive integer such that $a^k$mod p = a mod p for all integers a. Prove that p - 1 divides k - 1.

Exercise fermat numbers

Let $F_n$ be a Fermat prime number prove that $\gamma_{F_n}(2)=2^{n+1}$

Why are the first 5 Fermat numbers prime?

Proving a property of about the Fermat numbers

What is the connection between Fermat's Little Theorem and "Fermat Liars"?

Prove there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.

Modular Congruence of the Fermat Numbers

Non prime modulus of prime powers

Euler Totient of Fermat Numbers

primality of $\frac{(2^{19}+1)}{3}$ and $\frac{(2^{23}+1)}{3}$

Induction on Fermat Numbers: $F_n = \prod_{j=0}^{n-1}F_j+2$

$2^n + 1$ is prime $ \implies n$ is a power of $2$

If $F_m = 2^{2^m} + 1$ is prime (with $m \geq 1$), does it follow that $3 \mid \frac{F_m + 1}{2}$?

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