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2007 BAMO p4 integers x^2+xy+y^2 <= 2007, odd , not divisible by 3

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August 27, 2019
number theorydivisiblediophantine

Problem Statement

Let NN be the number of ordered pairs (x,y)(x,y) of integers such that x2+xy+y2≤2007x^2+xy+y^2 \le 2007. Remember, integers may be positive, negative, or zero! (a) Prove that NN is odd. (b) Prove that NN is not divisible by 33.
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