The Corner

Unexpected Encounter

So I’m sitting here reading the current (April ‘07) Mathematics Magazine, an article titled “Digit Reversal Without Apology,” when I come across this:

Sutcliffe left the following open question: Is there any base for which there is a 3-digit solution but no 2-digit solution? Two years later T.J. Kaczynski* answered Sutcliffe’s question in the negative. His elegant proof showed that…

The asterisked footnote just says: “Better known for other work.” Right.

(Digit reversal is just what it says. If you do it to 8712, you get 2178—which, miraculously, divides exactly into 8712. Same for 9801. These are the only 4-digit base-10 numbers for which this is true. How about different numbers of digits, expressed in different bases? Well, you’ll have to read the article. Or get in touch with Mr. Kaczynski over there in ADX Florence.)

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