If $a\equiv b \pmod{n}$ and the integers $a, b$, and $n$ are divisible by $d>0$ then $\frac{a}{d}\equiv\frac{b}{d} \pmod{\frac{n}{d}}$

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this is related to my homework right now, i just don't have someone to ask

If $a\equiv b \pmod n$ and the integers $a, b$, and $n$ are divisible by $d>0$ then $$ \frac{a}{d}\equiv\frac{b}{d} \pmod {n/d} $$

Welcome to Mathematics Stack Exchange. Cf. this question – J. W. Tanner Oct 28 '20 at 02:11 — J. W. Tanner, Oct 28 '20 at 02:11
Use \pmod{x} to get $\pmod{x}$. – Arturo Magidin Oct 28 '20 at 02:14 — Arturo Magidin, Oct 28 '20 at 02:14
@Darsen See Arturo's comment – Ben Grossmann Oct 28 '20 at 02:15 — Ben Grossmann, Oct 28 '20 at 02:15
Also If gcd(d,n}=1 you can write as a/d=c/dmod(n) – user600016 Oct 28 '20 at 02:23 — user600016, Oct 28 '20 at 02:23

score -1 · Answer 1 · answered Oct 28 '20 at 02:13

-1

Hint: $a \equiv b \pmod n$ means that there exists an integer $k$ for which $a - b = kn$.

answered Oct 28 '20 at 02:13

Ben Grossmann

1 Answers1