Lecture Notes Supplement, 11 Oct 2010

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Suppose Odd(7c–5) & show Even(c):

Because Odd(7c–5),
we know 7c–5 = 2j+1, for some j.

∴ 7c = 2j+6

∴ c = (2j+6) / 7

But then need to show (2j+6) / 7 = 2k, for some k

So, need to show k = (2j+6) / 14 = (j+3)/7

… and this doesn't seem to be leading us anywhere.

So, let's return to the proof and try a different strategy.

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