Prove that any odd number can be expressed as $$4n+1$$ or $$4n+3$$ I can see that this is true, but I am not certain on how to make a formal proof.
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Hint: Every odd number can be written as $2k+1$. Now $k$ can be even ($k=2n$) or...
drhab
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1Much more than perfection!! :) – Nov 02 '13 at 19:07
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... or $k$ can be odd? Can you explain a little further please? – user1090614 Nov 02 '13 at 19:28
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Indeed, odd. That is $k=2n+1$. What do you get if you substitute these possibilities for $k$ in $2k+1$? – drhab Nov 02 '13 at 19:30
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$2(2n+1)+1 = 4n+3$ and $2(2n)+1 = 4n+1$. sweet! – user1090614 Nov 02 '13 at 19:32