Copyright © University of Cambridge. All rights reserved.

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

Show menu

Circles for which the square of the radii are 5, 25, 125, 625 and 3125.

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.