# Let a=b (mod n) and c=d (mod n). Prove that ac=bd (mod n).?

### 1 Answer

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- jibzLv 68 months ago
By hypothesis there exist integers k and j such that

a = b + kn,

c = d + jn.

So

ac

= (b + kn)(d + jn)

= bd + bjn + knd + kjn²

= bd + (bj + kd +kjn)·n

= bd (mod n).

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