Fraction between fractions

Number Theory Level 4

Find the smallest value of the positive integer n n such that:

For each positive integer m < 2017 m<2017 there exists some integer k k such that

m 2017 < k n < m + 1 2018 \frac { m }{ 2017 } <\frac { k }{ n } <\frac { m+1 }{ 2018 }


The answer is 4035.

Linkin Duck by Linkin Duck , 33, Vietnam

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Keanu Ac
Jun 9, 2017

To find the smallest denominator that will be between 2017 and 2018 is 4035. This works because the minimum distance between any two integers is 1, multiplying both by 2 leaves one integer in between them.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...