Proof of Fermat’s theorem in a few lines

This article was drafted on 19-09-2011, but not publicized earlier.

Recently I had given a lot of proofs and corollaries of a new theorem that I called 50cent theorem, in this article:

I will use the general form to prove Fermat’s theorem in just a few line, a feat never acheived.

The idea of the theorem (50cent) is for every integer to it’s k-th power, there is atleast one integer (and unique when the power is close to the prime number in the theorem) in the (k-1)th vicinity of the k-th power of the integer which is an integer multiple of 5(in more generalization of a prime number close to the power k). (k-1)th vicinity means a difference from an integer within the scope of integers -(k-1), -k, .. 0, .., k, (k-1). ie. (a)^k = 5*m + P where P is any integer in the scope -(k-1), -k, .. 0, .., k, (k-1).

SO from the equation above it is clear that any k-power integer of an integer is a 5th multiple plus another integer, always.

Fermat’s Theorem: a^n + b^n = c^n is not valid, for higher powers than n=2.

LHS = 5*m_a + P_a + 5*m_b + P_b = 5*(m_a + m_b) + P_a + P_b, since P_a and P_b are integers in the same scope of integer n-1, they are equivalent although different.

RHS = c^n + P_b,

=> LHS is not equal to RHS unless one of the integer P_a or P_b is zero always.

This is valid till the prime number 5 is sufficient to test the powerfreeness of another integer. {m,n,k} are numbers/integers in the vicinity and for very high powers in Fermat’s theorem one needs higher prime numbers. This theorem has been evidently tested for small powers.

I am an experimental particle physicist, traveler, teacher, researcher, scientist and communicator of ideas. I am a quarkist and a bit quirky ! Hypothesis non fingo, eppur si muove, dubito cogito ergo sum are things that turn me on ! Researcher in experimental high energy physics (aka elementary particle physics; like “quarks, leptons & mesons and baryons”) … Teacher of Physics (and occasionally chemistry and maths) Blogger (check my website; mdashf.org) ! Love to read read and read but only stuff that interest me. Love to puff away my time in frivolities, just dreaming and may be thinking. Right now desperately trying to streamline myself.

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