P71
projecteuler.net

Ordered Fractions

ℹ️Published on Friday, 4th June 2004, 06:00 pm; Solved by 32397;
Difficulty rating: 10%

Consider the fraction, $\dfrac n d$, where $n$ and $d$ are positive integers. If $n \lt d$ and $\operatorname{HCF}(n,d)=1$, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for $d \le 8$ in ascending order of size, we get: $$\frac 1 8, \frac 1 7, \frac 1 6, \frac 1 5, \frac 1 4, \frac 2 7, \frac 1 3, \frac 3 8, \mathbf{\frac 2 5}, \frac 3 7, \frac 1 2, \frac 4 7, \frac 3 5, \frac 5 8, \frac 2 3, \frac 5 7, \frac 3 4, \frac 4 5, \frac 5 6, \frac 6 7, \frac 7 8$$

It can be seen that $\dfrac 2 5$ is the fraction immediately to the left of $\dfrac 3 7$.

By listing the set of reduced proper fractions for $d \le 1\,000\,000$ in ascending order of size, find the numerator of the fraction immediately to the left of $\dfrac 3 7$.



Soluzione

Last modified: May 01, 2025. Website built with Franklin.jl and the lovely Julia programming language.