 Subadditivity of the base-p digit sum

ID: subadditivity-of-the-base-p-digit-sum

For nonnegative integers

x

and

y

d_{p} (x + y) \leq d_{p} (x) + d_{p} (y) .

In column addition, every carry replaces

p

units in one digit by one unit in the next digit and therefore decreases the digit sum by

p - 1

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