List questions from prime-numbers

Published on 25 Mar 2026 - 13:28

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Factors of ${{x+n} \choose {n}}$

Published on 25 Mar 2026 - 12:26

99

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Sum of reciprocals of prime numbers, using alternating sings

Published on 25 Mar 2026 - 16:02

73

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Does concatenating the perfect powers ever lead to a prime?

Published on 25 Mar 2026 - 4:38

454

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Is the sequence of prime numbers a linear recurrent sequence?

Published on 13 May 2018 - 11:40

540

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For $n\ge4,$ prove that $F_n+1$ is not prime, where $F_n$ is $n^{th}$ Fibonacci number.

Published on 25 Mar 2026 - 7:45

37

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Prime factor $p$ of $10^{2^k}+ 1$ is $p \equiv 1 \pmod{2^{k+1}}$

Published on 13 May 2018 - 15:21

258

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$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

Published on 23 Mar 2026 - 12:23

4.5k

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How do I show that $n$ is prime if and only if $\phi(n) = n − 1$?

Published on 25 Mar 2026 - 13:55

346

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Show that if $x$ is a primitive root modulo $p^r$, then $x$ is a primitive root modulo $p$

Published on 25 Mar 2026 - 5:41

88

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Prove that for every prime number $|\{1\leq x \leq p^2 : p^2 | (x^{p-1}-1) \}|=p-1$

Published on 27 Mar 2026 - 1:04

55

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Prime factorization of numbers in $1+6N$ and $5+6N$?

Published on 25 Mar 2026 - 1:17

1.3k

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Proof about relatively prime numbers.

Published on 15 May 2018 - 3:06

78

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Property of prime integers mod 3

Published on 15 May 2018 - 12:52

85

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Can every positive integer $n > 2$ be written as the sum of $k$ prime numbers?

Published on 15 May 2018 - 17:12

List Question

Probability that a random number avoids a set of prime divisors

Factors of ${{x+n} \choose {n}}$

Sum of reciprocals of prime numbers, using alternating sings

Does concatenating the perfect powers ever lead to a prime?

Is the sequence of prime numbers a linear recurrent sequence?

For $n\ge4,$ prove that $F_n+1$ is not prime, where $F_n$ is $n^{th}$ Fibonacci number.

Prime factor $p$ of $10^{2^k}+ 1$ is $p \equiv 1 \pmod{2^{k+1}}$

$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

How do I show that $n$ is prime if and only if $\phi(n) = n − 1$?

Show that if $x$ is a primitive root modulo $p^r$, then $x$ is a primitive root modulo $p$

Prove that for every prime number $|\{1\leq x \leq p^2 : p^2 | (x^{p-1}-1) \}|=p-1$

Prime factorization of numbers in $1+6N$ and $5+6N$?

Proof about relatively prime numbers.

Property of prime integers mod 3

Can every positive integer $n > 2$ be written as the sum of $k$ prime numbers?

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