Question

If $2 \mid F_n$, then $4 \mid F_{n+1}^2-F_{n-1}^2$, where $F_n$ is $n$-th Fibonacci number

score 105 · Answer 1 · 2026-03-26 02:56:23

105

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If $2 \mid F_n$, then $4 \mid F_{n+1}^2-F_{n-1}^2$, where $F_n$ is $n$-th Fibonacci number

Published on 26 Mar 2026 - 2:56

score 63 · Answer 2 · 2018-10-28 12:39:26

63

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Polynomials with some special sum divisible by all linear polynomials

Published on 28 Oct 2018 - 12:39

score 55 · Answer 3 · 2018-10-28 21:20:25

55

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How to prove that for any natural number $n$, $10|(3^{2+4n}+1)$ using induction?

Published on 28 Oct 2018 - 21:20

score 1.2k · Answer 4 · 2018-10-28 23:46:33

1.2k

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What does it mean for an ideal in the ring of integers to divide another ideal in the ring of integers?

Published on 28 Oct 2018 - 23:46

score 102 · Answer 5 · 2026-03-23 09:09:03

102

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Is the repunit $R_{3^k}$ divisible by $3^k$?

Published on 23 Mar 2026 - 9:09

score 269 · Answer 6 · 2018-10-31 13:22:56

269

Views

$(n-1)! \equiv 0 \pmod n$, Wilson's Theorem version for non prime moduli

Published on 31 Oct 2018 - 13:22

score 171 · Answer 7 · 2018-10-31 18:55:53

171

Views

Prove that $10|n+3n^3+7n^7+9n^9$

Published on 31 Oct 2018 - 18:55

score 201 · Answer 8 · 2018-11-01 12:04:16

201

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Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

Published on 01 Nov 2018 - 12:04

score 89 · Answer 9 · 2018-11-01 16:12:24

89

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How to do 21/2 on paper

Published on 01 Nov 2018 - 16:12

score 1.4k · Answer 10 · 2018-11-02 06:18:44

1.4k

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How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?

Published on 02 Nov 2018 - 6:18

score 55 · Answer 11 · 2026-03-25 06:03:34

55

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Find largest $a, b \in \mathbb{N}$ so that $a \times b \geq n$

Published on 25 Mar 2026 - 6:03

score 296 · Answer 12 · 2026-03-25 21:48:46

296

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Prove that there are infinitely many integers $n$ such that $3\nmid\phi(n)$

Published on 25 Mar 2026 - 21:48

score 148 · Answer 13 · 2018-11-03 05:18:48

148

Views

Do consecutive integers never divide each other? If not, why?

Published on 03 Nov 2018 - 5:18

score 274 · Answer 14 · 2026-03-25 21:48:45

274

Views

Is the equation $x = \phi(n), x=2k, n,k \in \mathbb{Z}$, where $\phi(n)$ is the Euler totient function, solvable for all evens?

Published on 25 Mar 2026 - 21:48

score 639 · Answer 15 · 2026-03-25 13:33:18

639

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Divisibility of Consecutive Powers of 10

Published on 25 Mar 2026 - 13:33

List Question

If $2 \mid F_n$, then $4 \mid F_{n+1}^2-F_{n-1}^2$, where $F_n$ is $n$-th Fibonacci number

Polynomials with some special sum divisible by all linear polynomials

How to prove that for any natural number $n$, $10|(3^{2+4n}+1)$ using induction?

What does it mean for an ideal in the ring of integers to divide another ideal in the ring of integers?

Is the repunit $R_{3^k}$ divisible by $3^k$?

$(n-1)! \equiv 0 \pmod n$, Wilson's Theorem version for non prime moduli

Prove that $10|n+3n^3+7n^7+9n^9$

Find all primes $p$ and $q$ such that $p^2+1 | 2003^q+1$ and $q^2+1 |2003^p+1$.

How to do 21/2 on paper

How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?

Find largest $a, b \in \mathbb{N}$ so that $a \times b \geq n$

Prove that there are infinitely many integers $n$ such that $3\nmid\phi(n)$

Do consecutive integers never divide each other? If not, why?

Is the equation $x = \phi(n), x=2k, n,k \in \mathbb{Z}$, where $\phi(n)$ is the Euler totient function, solvable for all evens?

Divisibility of Consecutive Powers of 10

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