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Paper 2 · November 2009 · Proof by mathematical induction

In a proof by induction that $5^{2n}-3^{2n}$ is a multiple of 8 for every positive integer $n$ , the first step is to test $n=1$ . Evaluate $5^{2n}-3^{2n}$ when $n=1$ .

Model answer

16

Also accepted: 5^2-3^2=16

Explanation

When

n=1

,

5^{2n}-3^{2n}=5^{2}-3^{2}=25-9=16

, and

16=8\times2

, so the statement holds for

n=1

.

Derived from ZIMSEC Mathematics Paper 2, November 2009, Q1

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