# Diophantine Equation a(3b+1)=c

1. Sep 13, 2010

### danieldf

a(3b+1)=c
The solutions are obvious. I want to know if there is a solution a(n), b(n) (and so, c(n)) or at least a solution a(b).
Can someone help with that..?

Last edited: Sep 13, 2010
2. Sep 13, 2010

### danieldf

Sorry.. I didn't explain before.

3. Sep 15, 2010

### ramsey2879

What do you mean by "a(n), b(n) (and so, c(n))" ?

4. Sep 15, 2010

### danieldf

I mean a solutions in one variable. Like (2n, n²-1,n²+1) is a solutioin for x²+y²=z²

5. Sep 16, 2010

### ramsey2879

There are an infinite number. The only comprehensive one of all possibilities though is
a = F(n), b = G(n), so c= F(n)*(3G(n)+1). Simple as that.

Last edited: Sep 16, 2010