Hi Math Forum,
Any one have any solutions for this:
Prove by induction: that for every positive integer n, 4^n +14 is congruent to 0 (mod 6).
I been at it for days, any help would be greatly appreciated
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Originally Posted by brainspasm Prove by induction: that for every positive integer n, 4^n +14 is congruent to 0 (mod 6). You do realize that means is divisible by six for each n?
Clearly it is true for . No?
Suppose that it is true for now prove it is true for .
Look at this .
Is that a multiple of six?
it's no so much an induction problem but a problem related to equivalence classes, note:
Why does: ?
And I think you're done.
Last edited by bmp05; February 6th 2010 at 08:05 AM.
Reason: latex funkiness
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