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Old 11-17-2019, 10:57 PM
Left Hand of Dorkness's Avatar
Left Hand of Dorkness is offline
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I dunno if this is helpful, but you can rule out any pair in which both numbers are even. The squares of an even number will always be even, the product of two even numbers will always be even, and the difference between the squares of two even numbers will always be even. So you can't have a2 - b2 = ab 1, since that would lead to one result or the other being odd.

If one number's odd and the other is even, their product will be even, and the difference between the squares will be odd, so that can work. And if both are odd, then the product will be odd, and the difference between the squares will be even, so that can work. But no pairs of even numbers would work.

Edit: The hint tells you one of the numbers is prime, which means all that work is superfluous: that means one of the three-digit numbers must be odd. D'oh!

Last edited by Left Hand of Dorkness; 11-17-2019 at 10:59 PM.