Are there any positive and/or negative integer solutions for a, b, c in the following equation?
a/b + b/c + c/a = 1
My computer locked up right before posting a proof but the answer is no. To prove this first assume a,b,c > 0 then show that the result > 1. Then assume a,b,c < 0 and get the same result. Then assume without loss of generality a<0, b,c > 0 and go through the cases b<c, b=c, b>c and show for each case that the resulting equation cannot equal 1. Then show without loss of generality that a,b < 0, c>0 gives the same result.