P.T .
n4 + 4n is not a prime , for all integral values of n.
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3 Answers
62n4 + 4n
=n4 + 4n + (2nn2)2 - (2nn2)2
=(n2 + 2n)2 - (2nn2)2
I guess no one is interested in the Olympiad stuff :)
1we can use the sophie germain identity.
(a4 + 4b4) = (a2 + b2 +2ab )(a2+b2 -2ab)
this is obvuisly tru for even n.
thus for odd n
put n =2k+1
(2k+1)4 + 4(2k+1) = (2k+1)4 + 4.42k
this can be factorised as shown by teh identity . thus it's not a prime.
62wow.. i guess i just wrote one step more..
u learnt it as a theorem.. i just figured out the proof for the theorem :D