period0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,…
Let n be a positive integer, and let the function fn:N→{0,1} be defined by
fn(m)={01gcd(n,m)>1gcd(n,m)=1.
That is, fn(m) tells us whether m is coprime to n or not. If we write out the values of fn, we get a periodic (repeating) pattern. For instance, the list above gives the values of f10 starting at m=0; the pattern repeats itself with period 10.
Consider the function f1400. What is its period?
Note: The period is defined as the smallest possible value, that is, the least positive T such that fn(m+T)=fn(m) for all integers m.
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