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.

associative property of multiplication

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

283 square feet

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