Thread: Diophantine problem View Single Post
 2008-04-30, 22:52 #1 philmoore     "Phil" Sep 2002 Tracktown, U.S.A. 22·32·31 Posts Diophantine problem This problem was posed in the April 2008 issue of The American Mathematical Monthly by Jeffrey Lagarias, U. of Michigan: Determine for which integers $a$ the Diophantine equation $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{a}{xyz}$ has infinitely many integer solutions $(x,y,z)$ such that $\gcd(a,xyz)=1$. I have not solved it, I have just found it interesting and suspect that others on this forum might find it interesting as well.