# I Mobius Behaving Pair

1. Dec 19, 2016

### Gear300

Hello friends from afar.

Given the Möbius function μ(n), prove that if

,

then

.

(The upper bound for both sums is the integer floor of x.)

I've done the proof and it seems sound, but it also seems that the converse statement is true, implying that f and g should behave similar to a Mobius pair. But there was no question for the converse statement, so I just wanted confirmation. Many thanks.