Solutions for x2+y2=2007 and reference request.

manpreet Best Answer 3 years ago

I have never formally studied number theory, it is not a part of my course work, and what I have learnt is reading Wikipedia or the answers here. This question was on a test and I tried to use quadratic residues to solve this.

Find the number of solutions in integers to:

We can observe that 2007≡0(mod3)2007≡0(mod3)

x2≡0,1(mod3)x2≡0,1(mod3), y2≡0,1(mod3)y2≡0,1(mod3)

Since these can never add up to 33,we conclude that xx, yy are divisible by 33

Let x=3x′x=3x′, y=3y′y=3y′