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March 24th, 2017, 05:35 AM   #11
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$a,\ b \in \mathbb N^+\ and\ a + b = 10 \implies (10t + a)(10t + b) =$

$100t^2 + 10t(a + b) + ab = 100t^2 + 100t + ab = 100 * t(t + 1) + ab \implies$

$(10t + 5)^2 = 100 * t(t + 1) + 25.$

One general rule and a specific consequence. Not limited in theory to two and three digit numbers.
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