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40 analysis/period.p




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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.

 

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