Let [tex]n \geq 2[/tex] be an integer such that [tex]2^n + n^2[/tex] is prime. Prove that [tex]n \equiv 3(mod 6)[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

Ok this is what i have so far.

[tex]n \equiv 3(mod 6)\\ \Rightarrow 6|n-3\\ \Rightarrow n - 3 = 6k \\ \Rightarrow n = 6k + 3 \\[/tex].

Ok well i think i can use a proof by contradition. Obviosly [tex]n[/tex] cannot be an even number because [tex]2^n + n^2[/tex] wont be prime. So [tex]n[/tex] must be [tex]6k + 1[/tex] or [tex]6k + 3[/tex] or [tex]6k + 5[/tex]. Now when i plug all these into [tex]2^n + n^2[/tex] and mess around with it for a bit i just can't seem to prove it. Can anyone help me out?

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# Help with a proof.

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