Solutions for x2+y2=2007 and reference request.

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manpreet Tuteehub forum best answer Best Answer 2 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:

 

x2+y2=2007x2+y2=2007

 

We can observe that 20070(mod3)2007≡0(mod3)

x20,1(mod3)x2≡0,1(mod3)y20,1(mod3)y2≡0,1(mod3)

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

Let x=3xx=3x′y=3yy=3y′

 

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