MathDB
2016 Guts #22

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December 24, 2016

Problem Statement

On the Cartesian plane R2\mathbb{R}^2, a circle is said to be nice if its center is at the origin (0,0)(0,0) and it passes through at least one lattice point (i.e. a point with integer coordinates). Define the points A=(20,15)A = (20,15) and B=(20,16)B = (20,16). How many nice circles intersect the open segment ABAB?
For reference, the numbers 601601, 607607, 613613, 617617, 619619, 631631, 641641, 643643, 647647, 653653, 659659, 661661, 673673, 677677, 683683, 691691 are the only prime numbers between 600600 and 700700.
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