Question

Give a counterexample to the claim that if ax ≡ ay mod n then x ≡ y mod n.

Answer 1

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lets suppose a=3 x=1, y=2 n=3

then the claims says

ax = ay mod n

3*1 = 3*2 mod 3

3= 6 mod 3

0 = 0 mod 3 true

then x=y mod n

==> 1=2 mod 3 which is false