Diophantine Equationsmedium
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In the ring of integers of the quadratic field Q(2)\mathbb{Q}(\sqrt{2}), the norm of an element a+b2a + b\sqrt{2} is defined as N(a+b2)=a22b2N(a + b\sqrt{2}) = a^2 - 2b^2. Which of the following is an integer solution (a,b)(a, b) to the norm equation a22b2=7a^2 - 2b^2 = 7? (Select all that apply)