(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]2^{2n-1} + 3^{2n-1} is a number divisible by 5.[/itex]

Prove by induction.

2. Relevant equations

3. The attempt at a solution

Firstly, solving for n = 1 is true.

I've re-written the statement to be:

[itex]2^{2n-1} + 3^{2n-1} = 5L[/itex]

where L is any natural number.

Now, I assume that it is true for n = k, and then show that if that is so, then it must be true for k + 1.

My problem, is that I don't know what to do to the right side of the equation here to keep a valid statement.

[itex]2^{2k-1} + 3^{2k-1} = 5L[/itex]

[itex]2^{2k+1} + 3^{2k+1} = 5L????[/itex]

What do you do to 5L to keep a valid equation?

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# Difficult induction proof

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