From f (x+13/42)+f (x) = f (x+1/7)+f (x+1/6).

1 . f(x+ 1/6+ 1/7)-f(x+ 1/6)= f(x+ 1/7)-f(x)

Let g(x)=f(x+ 1/7)-f(x) then g(x+ 1/6)=g(x).

2 . f(x+ 1/6+ 1/7)-f(x+ 1/7)= f(x+ 1/6)-f(x)

Let h(x)=f(x+ 1/6)-f(x), then h(x+ 1/7)=h(x).

If it can be determined that 1/6 and 1/7 are the periods of f(x), the maximum value of the minimum positive period of f(x) is 1/42.

Although I can't prove or give a counterexample, I feel that from

G(x)=f(x+ 1/7)-f(x) is a periodic function, which means that f(x) is also a periodic function.

Actually:

From the equation f (x+13/42)+f (x) = f (x+1/7)+f (x+1/6), if 13/42,/kloc.

For example, f(x)=c(c is a constant) is a periodic function, and any non-zero number is its period, so this function meets the requirements. I'm thinking that I can even give a function that is not a periodic function to meet the above conditions.