A number theory problem by A Former Brilliant Member
How many ordered pairs are such that their highest common factor is and lowest common multiple is ?
The answer is 0.
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
The greatest common denominator of two integers will always divide their least common multiple. But 1 4 n + 2 4 2 n + 7 = 3 + 1 4 n + 2 1 which is never an integer for any integer n . Hence there are no solutions.