Is There a Single-Variable Solution to This Diophantine Equation?

[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..?

 

[danieldf]

Sorry.. I didn't explain before.

 

[ramsey2879]

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..?

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

 

[danieldf]

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

 

[ramsey2879]

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

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.