Representations by a Sum of Squares

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Lagrange proved that every positive integer can be written as the sum of four or fewer squares. Click a number to display the number of ordered positive sum of squares representations and the total number of representations. Equivalent distinct representations are listed as tooltips by the disk under that number. Numbers having square representations are marked in individual black and white views. The colored view combines these special views to indicate similarities between numbers.

Contributed by: Michael Schreiber (March 2011)
Open content licensed under CC BY-NC-SA


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