practice problems pending

Q1. Find integer solutions for x^2 + y^2 = 2025
S1.
Mod 9 of a square gives 0,1,4,7
Here RHS is 0. For LHS to be 0, both have to give mod 0.
=> x = 3a, y = 3b
=> a^2 + b^2 = 225
Again mod 9 is 0
a = 3c, b = 3d
c^2 + d^2 = 25

(c,d) = (0,+-5) (-+5,0) (-+3,-+4) (-+4,-+3)
Total solutions = 2 + 2 + 4 + 4 = 12
To find actual solutions multiply c,d with 9.

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