Thread: Number Theory - Multiplicative Functions

Another one of those interesting number theory questions:

Originally Posted by moolimanj

Another one of those interesting number theory questions:

F(7)=5
F(8)=0
F(9)=3
F(12)=0.
Is it right?

Keep Smiling
Malay

Now if is even, say then any two adjacent ones you take we have one is even and one is odd. Thus cannot be both 1 because at least one of them is at least 2.

For the converse consider and pick the first two and so we know that but since it means (otherwise ) and so it has to be which means .

If prime then in the integers we see that . Thus we have cases.