More Authentic Proof of Fermat Number that it is composite for n > 4 [ ]


This is the extended version of my earlier publication in this journal i.e. for the month of June edition 2015. I mentioned there that the proof of Fermat number to be composite beyond n = 4 is fully based on a conjecture that if u2 + 1 is composite, u4 + 1 is also composite. This conjecture was proved by the property of N-equation which was published in August edition 2013. To prove this conjecture I considered the fact that (u4 + 1) satisfies only the left hand odd element of a second kind N-equation a2 + b2 = c2. But (u4 + 1) may also satisfy the left hand odd element of a first kind N-equation except k = 1. This paper includes the fact that in both the cases the proof remains undisturbed. Because all the left hand odd elements except k = 1 are composite.