oh. my. god.

I think 121 is a perfect square in base anything greater than 2, simply because there’s no such thing as a 2 in base 2.
1001, though, is a “transliteration” of 121 into base 2, and it’s still a square.

hehe–and it seems to work for 1331 and 14641 tooo…

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6 thoughts on “

  1. Alas, parece que hay un misunderstanding.
    You don’t actually take “121” and make it (1 1 1 1 1)”base three,” but just put in the digits “(1 2 1)’base three'”.
    (1 2 1) in base 3 means 1(3^2) plus 2(3^1) plus 1(3^0), which is..16 base 10, I think.
    It works because (1 2 1) in base anything bigger than 2 equals:
    1(b^2) + 2(b) + 1, which equals (b+1)^2. So 121 in base..29 is 900, or 30 squared, just by that rule.
    *prays that self is correct and hasn’t said anything idiotic while pretending to know basic algebra and number theory*

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