List questions from divisibility

Published on 12 May 2015 - 17:06

38

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Given $2^n$, what is the largest power of $2$ that will divide any random concatenation of base $10$ digits of powers of $2$ ending with $2^n$?

Published on 10 Apr 2026 - 19:25

110

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Multiple of power of 5 with only the digits 2,5,6

Published on 11 Apr 2026 - 19:47

84

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Divisibility of numbers

Published on 09 Apr 2026 - 22:15

87

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Mysterious divisibility condition showing up in computation of determinant of certain sparse matrices

Published on 14 May 2015 - 19:05

492

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Show that if $p$ is a prime number and $a$ is an integer, and if $p \mid a^2$ , then $p \mid a$.

Published on 31 Mar 2026 - 19:17

214

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What is the biggest $n$ in $4^n$ that divides $7^{2048} - 1$?

Published on 15 May 2015 - 15:03

93

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Divisibility number theory problem

Published on 10 Apr 2026 - 0:04

76

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For what values of $n$ , does $7 \mid 5^n+1$

Published on 15 May 2015 - 22:40

1.7k

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Why 9 mod -7 = -5? Quotient and remainder with negative integers.

Published on 27 Mar 2026 - 18:34

763

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If the sum of two squares is divisible by $7$, both numbers are divisible by $7$

Published on 10 Apr 2026 - 14:56

211

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How to find the remainder of polynomial division?

Published on 16 May 2015 - 22:44

1.1k

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How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?

Published on 17 May 2015 - 16:34

203

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Solving a Diophantine equation3

Published on 08 Apr 2026 - 3:16

6.9k

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Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$

Published on 02 Apr 2026 - 21:37

List Question

Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?

Given $2^n$, what is the largest power of $2$ that will divide any random concatenation of base $10$ digits of powers of $2$ ending with $2^n$?

Multiple of power of 5 with only the digits 2,5,6

Divisibility of numbers

Mysterious divisibility condition showing up in computation of determinant of certain sparse matrices

Show that if $p$ is a prime number and $a$ is an integer, and if $p \mid a^2$ , then $p \mid a$.

What is the biggest $n$ in $4^n$ that divides $7^{2048} - 1$?

Divisibility number theory problem

For what values of $n$ , does $7 \mid 5^n+1$

Why 9 mod -7 = -5? Quotient and remainder with negative integers.

If the sum of two squares is divisible by $7$, both numbers are divisible by $7$

How to find the remainder of polynomial division?

How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?

Solving a Diophantine equation3

Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$

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