Math Is Fun Forum

Faye16

Guest

discrete mathematics?

Construct a binary operation on the non-negative integers Z+ such that 
for any n in Z+, the equation a * b = n has exactly one solution for a 
and b.

Thanks for the help=)

Candide

Member

Registered: 2010-09-30

Posts: 3

Re: discrete mathematics?

Seems a little trivial but

n=1 has only one solution for a and b

1*1=1

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: discrete mathematics?

Bit messy, but I think this one works:

a * b = { (a-1)² + b, if a > b
           { b(b-1) + a, otherwise

Here's how to start "counting" using this system.

1*1 = 1
2*1 = 2
1*2 = 3
2*2 = 4
3*1 = 5
3*2 = 6
1*3 = 7
2*3 = 8
3*3 = 9
4*1 = 10
...

---

Why did the vector cross the road?
It wanted to be normal.