Discussion

What is the remainder when the product \(121 \times 122 \times 123\) is divided by 7?

Answer: A

Correct answer: 3

Reduce each factor modulo 7 before multiplying, rather than forming the product first.

\[121 = 7\times 17 + 2,\qquad 122 = 7\times 17 + 3,\qquad 123 = 7\times 17 + 4\]

So the product is congruent to \(2\times 3\times 4 = 24\), and \(24 = 7\times 3 + 3\).

\[121\times 122\times 123 \equiv 3 \pmod 7\]

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