Assume 8-bit bytes and strings composed of 1 byte per
character. For an unsigned integer stored in *n*
bytes prove:

(a) 3*n* bytes will always provide enough space
to
hold the decimal string representation of the integer.

(b) 3 is the smallest coefficient to provide enough
storage
for all values of *n*.

I know this to be true but proving (a) is harder than I thought.