1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.

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Q: Prove that for all natural numbers k, a (5*2^(2k+1) - 1)/3 + a*4^k is of the form 5 + 6a.

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Q: Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a

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Q: (4) For all natural numbers n, 4^n - 1 is a multiple of 3

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Q: Prove that for all natural numbers k, (4^k - 1)/3 is an odd number.

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