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To prove by Principle of Induction.

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Prove using the Principle of Induction.

5^(2n)-4^n is divisible by 7 for any positive integer n.

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Solution Summary

Using the Principle of Induction to prove that some expression depending on integer number n is divisible by 7 for every positive integer n.

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Proof.

For n=1 we have

5^2-4^1=25-4=21=3*7. So divisible by 7.

Suppose the property is true for n=k, ...

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