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Prove that if x, y, z are intergers such that 5*x^2 + y^2 = 7*z^2, then x, y and z are all divisble by 5.

So what I have done so far,

I have worked out 1, 2 ,3 , 4, and their squared to find that. the squared intergers of any interger will end in 0,1, 4 in modulo 5. (ps im not sure if im phrasing this write as well)

then the LHS would be 0, 1,4. whilst the right hand side will be 0, 2, 3.

now i dont know wher to go. can someone help me, or show me how to prove this.

would be greatly appreicated.

thanks