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# Mod arithmetic

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FInd the integer n, 0 <= n <= 11, such that n = 1089 (mod 12).

Apr 23, 2022

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Note that $$12 \times 90 = 1080$$.

Then, $$1089 = 12\times 90 + 9$$.

Taking mod 12 on both sides results in $$1089 \equiv 9 \pmod{12}$$.

Apr 23, 2022