Let $b$ be an integer greater than $2$, and let $N_b = 1_b + 2_b + \cdots + 100_b$ (the sum contains all valid base $b$ numbers up to $100_b$). Compute the number of values of $b$ for which the sum of the squares of the base $b$ digits of $N_b$ is at most $512$.
$100_b= 100$ (small low $b$) <<(im not sure what its called)
I honestly am so lost. I don't even know where to begin. Please help.