List questions from divisibility

Published on 16 Apr 2026 - 8:20

750

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

Published on 15 Apr 2026 - 0:07

50

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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 15 Apr 2026 - 11:18

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 10 May 2026 - 16:57

65

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Replace number by non-divisor

Published on 10 May 2026 - 14:47

395

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

Published on 10 May 2026 - 14:56

208

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

Published on 10 May 2026 - 20:36

465

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Palindrome multiple of prime

Published on 29 Apr 2026 - 12:51

181

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Is this number an integer?

Published on 11 May 2026 - 2:01

99

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Growth rate of number of divisors of Highly Composite Numbers

Published on 12 Apr 2026 - 15:25

123

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Proof of LCM property.

Published on 29 Apr 2026 - 12:51

339

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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 10 May 2026 - 20:44

72

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

Published on 10 May 2026 - 19:35

61

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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 10 May 2026 - 23:24

81

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

Published on 10 May 2026 - 14:49

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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