The Universe of Disco

A triviality about numbers that look like abbc

Looking at license plates the other day I noticed that if you have a four-digit number !!N!! with digits !!abbc!!, and !!a+c=b!!, then !!N!! will always be a multiple of !!37!!. For example, !!4773 = 37\cdot 129!! and !!1776 = 37\cdot 48!!.

Mathematically this is uninteresting. The proof is completely trivial. (Such a number is simply !!1110a +111c!!, and !!111=3\cdot 37!!.)

But I thought that if someone had pointed this out to me when I was eight or nine, I would have been very pleased. Perhaps if you have a mathematical eight- or nine-year-old in your life, they will be pleased if you share this with them.

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