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March 30th, 2018, 10:45 AM   #1
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A Problem

Solve in positive integers
$x^3+y^3+3xyz=z^3+2018$

This problem doesn't seem to be solvable because there are three variables in one equation. Could anyone provide some assistance? Please provide full solutions with justifications.
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March 30th, 2018, 02:00 PM   #2
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$(x+y-z)\cdot(x^2+y^2+z^2-xy+xz+yz)=2\cdot1009$
Thanks from greg1313 and JeffM1
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