# 40 analysis/period.p

## Description

This article is from the Puzzles FAQ,
by Chris Cole chris@questrel.questrel.com and Matthew Daly
mwdaly@pobox.com with numerous contributions by others.

# 40 analysis/period.p

What is the least possible integral period of the sum of functions

of periods 3 and 6?

analysis/period.s

Period 2. Clearly, the sum of periodic functions of periods 2 and

three is 6. So take the function which is the sum of that function of

period six and the negative of the function of period three and you

have a function of period 2.

This proves that a period-2 solution exists, but not that it is minimal.

Since we're talking about integers, the only lower possibility is 1.

But the sum or difference of a period-1 and a period-3 function must have

period 3, not 6, therefore 1 is indeed impossible.

Continue to: