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**Faye16****Guest**

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

Seems a little trivial but

n=1 has only one solution for a and b

1*1=1

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

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