Divisibility Check in different Moduli

Asked Nov 28 '18 at 19:58

Active Nov 28 '18 at 21:19

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So I'm working on modular arithmetic and encountered the following problem:

Assume that $(a \cdot b) \mod m = c$ and that I know $c$. Can I still check for divisibility of $c$ by $a$? A quick example tells me that checking whether $c \mod a = 0$ does not work:

$((29*200) \mod 512) \mod 29 = 23$

But is this check impossible if $m < a \cdot b$ or is there a way to find out whether $a | c$? Maybe if $m$ and $n$ are primes?

Thanks!

edited Nov 28 '18 at 21:19

asked Nov 28 '18 at 19:58

Aares

$a\cdot b \pmod m$ or $\pmod n$? – Maged Saeed Nov 28 '18 at 20:02
The question is not at all clear. Please give a concrete example. – Bill Dubuque Nov 28 '18 at 20:05
I edited the question, I hope it's clearer now. – Aares Nov 28 '18 at 20:13
You seek to solve $\ ax\equiv c\pmod{m}\ $ for which see this answer. – Bill Dubuque Dec 01 '18 at 16:30

Divisibility Check in different Moduli

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