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Using mathematical induction, what remainder is obtained when 3^(2n) is divided by 8 for every natural number n?

1. 2
2. 3
3. 7
4. 1

Correct answer: 1

Solution

3^(2n) = 9^n, and 9 = 8+1, so 9^n = (8+1)^n leaves remainder 1^n = 1 when divided by 8 for every natural n.

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