Prove: 52n-1 is divisible by 24 for all n N

Solution: (a) Proof by induction: For n=1, we have 52n - 1 = 24. Next, assume that the result holds for n=k. For n=k+1, we have the following expression. 52(k+1) - 1 = (52k)(52) - 1 = (52k)(25) - 25 + 25 - 1 = (52k - 1)(25) + 24 By the induction hypothesis, 24 is a factor of 52k - 1, and so it is follows that 24 is a factor of 52n - 1.
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Prove that : 5^2n – 1is always divisible by 24 for all n natural numbers
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