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(abab) + (cdcd) is a perfect square

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April 23, 2009

Problem Statement

Let m\equal{}\left(abab\right) and n\equal{}\left(cdcd\right) be four-digit numbers in decimal system. If m\plus{}n is a perfect square, what is the largest value of a⋅b⋅c⋅d a\cdot b\cdot c\cdot d?
<spanclass=′latex−bold′>(A)</span> 392<spanclass=′latex−bold′>(B)</span> 420<spanclass=′latex−bold′>(C)</span> 588<spanclass=′latex−bold′>(D)</span> 600<spanclass=′latex−bold′>(E)</span> 750<span class='latex-bold'>(A)</span>\ 392 \qquad<span class='latex-bold'>(B)</span>\ 420 \qquad<span class='latex-bold'>(C)</span>\ 588 \qquad<span class='latex-bold'>(D)</span>\ 600 \qquad<span class='latex-bold'>(E)</span>\ 750
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