Question 502955: Prove: if 4 divides mn, then m is even or n is even.
i saw that this was p implies q or r. so by cases this would be p implies q and p implies r. I used the contrapositive to work on the first case. [if m is odd then 4 doesnt divide mn] i get to a point where i get:
4 does not divide (2k+1)n. I said that this would be odd multiples of n (ie, 3n, 5n, ..., 45n,..., 99n,...) which if it produced an odd number, 4 wouldnt divide it. But this would be entirely contingent on what n is. [if even, then 4 could divide it; if odd, 4 wont divide it]
Should i just be proving the contrapositive of p implies q or r? that way i have what m and n will be?
Any help would be grateful! thanks!
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Assume that the statement was false; e.g. if 4 divides mn, then neither m nor n is even. But then mn would be either 1 or 3 mod 4 (mn odd), and mn does not divide 4, contradiction.
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