Math Induction Solution: Proving 5^(2n) - 1 is Divisible by 8

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SUMMARY

The discussion focuses on proving that the expression 5^(2n) - 1 is divisible by 8 using mathematical induction. The initial step verifies the base case for n=1, confirming divisibility by 8. The inductive step involves manipulating the expression for n=k+1, leading to a factorization that simplifies the proof. The final expression demonstrates that the original statement holds true for all integers n.

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Homework Statement



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5^(2n) - 1 divisible by 8.

The Attempt at a Solution



For n =1, it is div. by 8.
For n=k+1,

5^(2(k+1)) - 1
=25^(k+1) - 1


I am not quite sure if this is the final solution.
 
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Hi Kinetica! :smile:

Maybe you can start by factoring [itex]5^{2n}-1[/itex].
 
Hey! I got it! Thanks!

5^[2(k+1)] - 1
25*5^[2k] - 1
5^[2k] + 24*5^[2k] - 1
5^[2k] - 1 + 24*5^[2k]
 

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