Monday, 11 April 2016

elementary number theory - Prove that 24n+1 cannot be a prime if 3|n



24n+1 cannot be a prime if 3|n and n>0



My Try:

2^{12k}+1\equiv (-1)^{3k}+1 \equiv0\pmod{17}
So it divisible by 17 for odd k. But how to complete the proof?


Answer



Hint: 16^{3k} +1 = (16^k+1)(16^{2k}-16^k+1).


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