# Tagged Questions

This tag is for questions about divisibility, that is, determining when one thing is a multiple of another thing.

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### Prove that if $m\mid (a^2 -1)$ then $m\mid (a^4 -1)$

I have been stuck on this question for quite some time, I have tried several methods but to no avail. I attempted to use prime factorization but I couldn't really see where to go with it.
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### Expected number of digits of the smallest prime factor of $1270000^{16384}+1$

The number $N\ :=\ 1270000^{16384}+1$ with $100,005$ digits is given. Given, that $N$ is composite and does not have a prime factor below $2\times 10^{13}$, what is the expected number of digits ...
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### Let N be a four digit number, and N' be N with its digits reversed. Prove that N-N' is divisble by 9. Prove that N+N' is divisble by 11.

Let $N$ be a four digit number, and $N'$ be $N$ with its digits reversed. Prove that $N-N'$ is divisible by $9$. Prove that $N+N'$ is divisible by $11$. I let $N=abcd$ and $N'=dcba$ but I dont see ...
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### Prove that if a|b, c|d, then ac|bd [duplicate]

I'm trying to prove it, but I can't find how. If a divides b, and c divides d, then ...
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### Prove: If $n^2$ is odd, then $n$ is odd. [duplicate]

$n$ is a natural number. I want to prove that, if the square of $n$ is odd, then $n$ itself is odd. Any hints welcome and preferred. Thank you!
### Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$ [duplicate]
Show that if $a, b$, and $c$ are integers with $(a,b)=(a,c)=1$, then $(a,bc)=1$ I don't know exactly that I should use the division algorithm or $(a,b)=d$, $(a/d,b/d)=1$. This is my first time to ...