1that came once in isi entrance,,,too simple...na
*Prove that every integer of the form n^4+4 is always composite.........
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5 Answers
1anirban r u sure u have posted the prob right
i think u have tried to give sophie germein identity which tells n^4+4 is composite always,,,its prof is very easy
1(n^2)^2+4=(n^2+2)^2-4n^2=(n^2+2++2n)(n^2+2-2n)...
hope u got the solution,,,,look any of the factor can not be 1...prove it!
62There is a better generalization that we had done and has been asked in some olympiad too..
n4+4n is always composite.. if n>1