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Puzzles
121
Source:
Mathematical Circus
by Martin Gardner
Find a number base other than 10 in which 121 is a perfect square.
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This is true for any base larger than 2. This is because:
$$121_n = 1+2n+n^2$$ $$=(n+1)^1$$
Extension
Which other base 10 square numbers are always square in high enough bases?
Tags:
numbers
,
bases
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bases
sums
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numbers
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crossnumber
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expansions
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doubling
geometric means
division
perfect numbers
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algebra
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