Determine the smallest octal (base 8) perfect square which ends with 2011 (reading left to right). What are the next two smallest octal perfect squares with this property?

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

Pell

n*8^4+(2^5)^2+9=z^2
1033=z^2-n*64^2, alternatively:
1033=z^2-4096n
n=63, z=509; n=578,z=1539, n=1596; z=2557; n=3141,z=3587; n=5177, z=4605; etc

In octal:772011_8, 11022011_8, 30742011_8 etc.

Posted by broll on 2011-10-07 02:00:21