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A geometric representation of integral solutions of x2 + xy + y2 = m2
Abstract
More than a century ago, Norman Anning conjectured that it is possible to arrange 48 points on a circle, such that all distances between the points are integer numbers and are all among the solutions of the diophantine equation
x2 + xy + y2 = 72 132 192 312:
We shall obtain Anning's conjecture as a consequence of a far more general geometrical result.
Key words: Quadratic diophantine equations, quadratic forms, plane integral point sets.
