Determine the smallest positive integer, expressible as the sum of two nonzero perfect squares, whose base nine representation ends with 2011 (reading left to right). What are the next two smallest base nine positive integers with this property?

*** For an extra challenge, solve this puzzle without using a computer program.

The smallest positive integer that is expressible under the given conditions is:
27712₁₀ = 42011₉ = 136² + 96²

With the next two smallest being:
52011₉ = 34273₁₀ = 183² + 28²
and
62011₉ = 40834₁₀ = 197² + 45² = 195² + 53²

Posted by Dej Mar on 2012-01-15 04:49:22