# question from my math theory module

• Aug 13th 2008, 01:45 PM
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
• Aug 15th 2008, 01:08 AM
Opalg
Quote:

Originally Posted by linearalgebradunce
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 ... .