Burt Kaliski Jr. (@modulomathy)

4/25/12 6:43 PM

#math trivia for #April25: #116 is the sum of two squares in base 10. Are there any other bases for which this is true?

The value 116 is the sum of squares in any base in which 16 is also a square, because 100 is a square in every base (it is the square of 10). (This excludes base 1 or unary, which doesn’t have a 10, but it doesn’t have a 16 either.)

The value 16 is a square in many bases in which the representation is valid (i.e., where b > 6). These include 10, 19, 30, 43, etc.

Are there any bases where 16 is not a square, but 116 is still the sum of some other squares?

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