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The least non-negative remainder when 64 x 65 x 66 is divided by 67, is

Solution

✅ Correct Option: 1

Work modulo 67: 64≡−364\equiv -3, 65≡−265\equiv -2, 66≡−166\equiv -1.

Product ≡(−3)(−2)(−1)=−6≡67−6=61(mod67)\equiv (-3)(-2)(-1) = -6 \equiv 67-6 = 61 \pmod{67}.

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