Math Help - question from my math theory module

1. proving an equation has no integer solutions

show that 7x^2 - 35xy^7 + 5y^14 = 88 has no integer solutions.

i cant find any examples similar in my lecture notes and am unsure which theories i should use to show this

show that 7x^2 - 35xy^7 + 5y^14 = 88 has no integer solutions.

i cant find any examples similar in my lecture notes and am unsure which theories i should use to show this
Start by reducing the equation mod 5 and mod 7, to get
$2x^2\equiv3\pmod5$,
$5y^{14}\equiv4\pmod7$.
Then concentrate on the second of those two congruences ... .