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Precalculus Mathematics Homework Help
Simple proof regarding integers
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[QUOTE="Yosty22, post: 4993587, member: 460241"] [h2]Homework Statement [/h2] Show that if m and n are integers such that 4|m[sup]2[/sup]+n[sup]2[/sup], then 4|mn [h2]Homework Equations[/h2][h2]The Attempt at a Solution[/h2] Since 4 divides m[sup]2[/sup]+n[sup]2[/sup], then we can say that m[sup]2[/sup]+n[sup]2[/sup] = 4k, where k is an integer. I haven't done any mathematical proofs of any kind yet, but we were supposed to see if we could do this. I am kind of stuck as to where to go from here. The only thing I could think of is to try to introduce a m*n term into the equation m[sup]2[/sup]+n[sup]2[/sup] = 4k. To do this, I multiplied and divided the left-hand side of the equation by mn to get: mn(m[sup]2[/sup]+n[sup]2[/sup]/mn) = 4k. Since I am looking to show that 4|mn, or mn = 4*(some integer), I tried to isolate the mn term. That means 4k/(m[sup]2[/sup]+n[sup]2[/sup]/mn) = mn, or 4kmn/(m[sup]2[/sup]+n[sup]2[/sup]) = mn. However, I don't think this proves anything. Any advice on how to proceed (or even where to start)? Thanks. [/QUOTE]
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Simple proof regarding integers
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