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philmoore · 2008-04-30, 22:52

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.

2008-04-30, 22:52	#1
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 10001011110₂ 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.