On The Exceptional solutions of Je\'smanowicz' conjecture
Abstract
Let (a,b,c)be a primitive Pythagorean triple. Set a=m^2-n^2b=2mn and c=m^2+n^2with mand npositive coprime integers, m>n and m \not \equiv n \pmod 2 A famous conjecture of Jeśmanowicz asserts that the only positive solution to the Diophantine equation a^x+b^y=c^zis (x,y,z)(2,2,2).In this note, we will prove that for any n>0there exists an explicit constant c(n)>0such that if m> c(n) then the above equation...
Paper Details
Title
On The Exceptional solutions of Je\'smanowicz' conjecture
Published Date
Oct 15, 2020
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