Foxmaths! 2.0

July 10, 2008

Zeroless Squares

Filed under: Maths — Tags: , — Fox @ 5:46 am

This is really a return to a problem I addressed over a year ago. It came up again, quite by chance, and I came up with another proof that makes my original post … almost embarrasing.

The idea is that for n = 0, 1, 2, 3, …, for numbers of the form

\frac{10^n + 2}{3}

their squares contain no zeroes.

For example, for n = 1, (10 + 2)/3 = 4, and 4*4 = 16, 16 contains no 0’s. But the same holds for -all- n, none of the squares contain 0’s.
(more…)

Blog at WordPress.com.