Abstract :
Using several currently available techniques, including Bakerʹs method, Frey curves and modular forms, we prove that for odd values of k with 1less-than-or-equals, slantk<170, the equation1k+2k+cdots, three dots, centered+xk=y2n in positive integers x,y,n with n>2 has only the trivial solution (x,y)=(1,1).
