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In building my current math study tables – from which the graphs in the previous post came – I encountered the number 385, which, as a direct consequence of its factoring into two factors in exactly four different ways, also has four different expressions as the difference of two squares. This in itself is not unusual, but the three non-trivial factorizations into a*b, which are 5*77, 7*55, and 11*35, produce expressions which are each a two-digit prime squared minus a multiple of twelve squared. Pretty! It might have to do with 385 being 12*32-1, but still, it was a pleasant structural surprise.

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