# Solve the following Diophantine equation for the integers, x and y.

Solve

$x^{7}+x^{6}y + x^{5}y^{2} + x^{4}y^{3} + x^{3}y^{4}+ x^{2}y^{5}+xy^{6} +y^{7} =234,567,890,122$

for integers, $x$ and $y$.

Remark: Two important equations,  x = βy  and d = |x – y|, help us to establish halting criteria for our algorithm…

What types of Diophantine equations are unsolvable?

Good Luck!

Dave.