Who even needs the binomial theorem?
(20+25)²=2025
(30+25)²=3025
(68320+14336)²=6832014336
(60494+17284)²=6049417284
and so on.

@jsiehler I tried:
(2125+4231)²=40398736. Does this only work for cherry picked numbers?

@AskChip Yes... actually, finding pairs of numbers that do this makes a nice little puzzle. They are not common.

@ZacharyHerold You can find these systematically using modular arithmetic and, particularly, the Chinese Remainder Theorem. It's not particularly nasty, though you'd want to have a computer or calculator handy if you're going to try to find bigger examples like (1975308+2469136)².

Now I found a related article in
oeis.org/A102766
. It's seem to relate 「Kaprekar number」 en.wikipedia.org/wiki/Kaprekar . It's new to me. Thanks!

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