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Prove SG's theorem (Posted on 2016-07-12) Difficulty: 2 of 5
Prove that a4+4 is never prime for any a bigger than 1.

No Solution Yet Submitted by Ady TZIDON    
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Solution and related result Comment 3 of 3 |
For two values that differ by two, their values in the expression always have a common factor:

[(n+1)^4-4]-[(n-1)^4+4]=8n^2+8n=8n(n^2+1)

This n^2+1 is a common factor:

13^4+4=5*29*197
15^4+4=197*259
14^2+1=197

So since a=2 and a=3 are not prime, not greater values of a can yield primes.

  Posted by Jer on 2016-07-13 10:20:51
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