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The diophantine equation (<i>X</i>[<i>X</i> − 1])<sup>2</sup> = 3<i>Y</i>[<i>Y</i> − 1]
The object of this paper is to prove that the only non-trivial solution in positive integers of the equation of the title is X = 3, Y = 4. Substituting x = 2 X – 1, y = 2 Y – 1 gives with a little manipulation