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## 'Square Pair Circles' printed from http://nrich.maths.org/

All powers of 5 can be written as the sum of two square numbers
in different ways. Investigate the number of points with integer
coordinates on circles with centres at the origin for which the
square of the radius is a power of 5. For the two circles shown in
red in the diagram the radius is a power of 5 and for the circles
shown in black this is not so but the square of the radius is a
power of 5.