Problem 383

Divisibility comparison between factorials

Let f_{5}(`n`) be the largest integer `x` for which 5^{x} divides `n`.

For example, f_{5}(625000) = 7.

Let T_{5}(`n`) be the number of integers `i` which satisfy f_{5}((2·`i`-1)!) 5(`i`!) and 1 `i` `n`.

It can be verified that T_{5}(10^{3}) = 68 and T_{5}(10^{9}) = 2408210.

Find T_{5}(10^{18}).

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