List questions from divisibility

Published on 21 Mar 2018 - 7:26

747

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How can I determine the smallest quotient for all general cases?

Published on 22 Mar 2018 - 10:33

47

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$p$ is prime and $n>1$ integer such that $p|{n \choose k} , \forall 1\le k \le n-1$ , then $n$ is a power of $p$?

Published on 22 Mar 2018 - 18:52

1.3k

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Find all integers $n$ such that $\frac{(n^2-n-1)^2}{2n-1}$ is a positive integer

Published on 22 Mar 2018 - 22:40

62

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Replace number by non-divisor

Published on 25 Mar 2026 - 4:44

392

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Prove that $F_{125n}$ is divisible by $125$.

Published on 25 Mar 2026 - 4:40

204

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$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$

Published on 23 Mar 2018 - 21:21

458

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Palindrome multiple of prime

Published on 20 Mar 2026 - 9:13

176

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Is this number an integer?

Published on 24 Mar 2018 - 8:22

96

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Growth rate of number of divisors of Highly Composite Numbers

Published on 24 Mar 2018 - 9:11

118

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Proof of LCM property.

Published on 20 Mar 2026 - 6:36

335

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If $\gcd(m,15)=\gcd(n,15)=1,$ show that $15\mid (m^4+n^4)$ or $15\mid (m^4-n^4)$.

Published on 24 Mar 2018 - 20:19

68

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On the conjecture that $12\mid t_n + t_{n+1}$.

Published on 25 Mar 2018 - 9:34

57

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For which positive integers $k$ dividing $4p^3$, does the equation $x^3+px=k^2$ has an integer solution in $x$?

Published on 25 Mar 2018 - 17:00

79

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Show that $a_n$ is divisible by 4 for all integers $n \geq 1.$

Published on 24 Mar 2026 - 23:56

List Question

If a, b, c and r are integers suppose $a=bq+r$ prove the following statement:$~~gcd(a,b)=gcd(b,r)$

How can I determine the smallest quotient for all general cases?

$p$ is prime and $n>1$ integer such that $p|{n \choose k} , \forall 1\le k \le n-1$ , then $n$ is a power of $p$?

Find all integers $n$ such that $\frac{(n^2-n-1)^2}{2n-1}$ is a positive integer

Replace number by non-divisor

Prove that $F_{125n}$ is divisible by $125$.

$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$

Palindrome multiple of prime

Is this number an integer?

Growth rate of number of divisors of Highly Composite Numbers

Proof of LCM property.

If $\gcd(m,15)=\gcd(n,15)=1,$ show that $15\mid (m^4+n^4)$ or $15\mid (m^4-n^4)$.

On the conjecture that $12\mid t_n + t_{n+1}$.

For which positive integers $k$ dividing $4p^3$, does the equation $x^3+px=k^2$ has an integer solution in $x$?

Show that $a_n$ is divisible by 4 for all integers $n \geq 1.$

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