For all, like me, wondering what a Diophantine equation actually is:

Diophantine equation
(from: britannica.com who seem to hand out far too many cookies.)

[An] equation involving only addition, multiplication, or taking power
+s in which all the constants are
natural numbers or their negatives and the only solutions of interest 
+are natural numbers or their
negatives. Named in honour of the 3rd-century Greek mathematician Diop
+hantus of Alexandria,
these equations were not systematically solved until the 7th century b
+y the Hindus.
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Maybe a maths type person can elaborate.