Question 13
We call a number pal if it doesn't have a zero digit and the sum of the squares of the digits is a perfect square. For example, $2115522$ is pal (because $2^2 + 1^2 + 1^2 + 5^2 + 5^2 + 2^2 + 2^2 = 8^2$) but $304$ and $12$ are not pal.
a. What is the greatest two-digit pal number?
b. Does there exist a $2011$-digit pal number?
a. What is the greatest two-digit pal number?
b. Does there exist a $2011$-digit pal number?