证明there are no natural numbers m and n such that 7/17 = (1/m) + (1/n).

证明there are no natural numbers m and n such that 7/17 = (1/m) + (1/n).

m,n are natural numbers, so that (1/m) + (1/n)=(m+n)/mn and we know that 7 can be writen by 1+6,2+5,3+4, by reason of symmetry of m and n,we ignore the other m+n permutations 4+3 5+2 6+1. and 1*6=6 2*5=10 3*4=12 and cant be a multiplier of 17(in fact 17 is premier.)even if m+n=7k mn=17k. note that k is a random positive natural number. we can establish a equation n^2-7kn+17k=0 which dont have natural number as roots.