#math trivia for #April30: #121 is the square of 11 in every base > 1 except which one? What’s the square of 11 in that base?

— Burt Kaliski Jr. (@modulomathy) April 30, 2012

The only base > 1 in which 121 is not a square of 11 is the base in which 121 is not a number: base 2.

In base 2, the square of 11 is 1001. (In decimal, we’d say the square of 3 is 9.)

In every other base b > 1, the square of 11 is the square of (b+1), which is b^2+b+1, or 121 in the base.