Can someone point out the error in the following "proof":(adsbygoogle = window.adsbygoogle || []).push({});

Prove a^n + b^n =/ c^n for n>2, a,b,c>1 (=/ means not equal to)

Let b=xa where x>1 and is from the set of real numbers generated by fractions, such that b is an integer

so:

a^n + (xa)^n =/ c^n

Expanding

a^n + x^n.a^n =/ c^n

then, taking the common factor a^n out

a^n(1+x^n) =/ c^n

then dividing through by a^n

1+x^n =/ c^n/a^n

Substitute y from the set of real numbers given by the fraction c/a, then

1+x^n =/ y^n

or:

y^n - x^n =/ 1

Factorizing:

x^n - y^n = (x - y)*(x^[n-1] + x^[n-2]*y + ... + y^[n-1]).

If the left side equals 1, then x > y, and x - y must be a positive

divisor of 1, namely 1. Then x = y + 1. Substitute that into the

second factor above, and set that second factor also equal to 1. That

should give you a contradiction. The contradiction means that the

assumption that the left side equals 1 must be false, and then you're

done.

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# Simple proof of Fermat's theorem?

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