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

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SUMMARY

The discussion centers on the Diophantine equation a(3b+1)=c and the search for single-variable solutions. Participants clarify that solutions can be expressed as functions of a single variable, specifically a(n) and b(n), leading to c(n). The comprehensive solution is identified as a = F(n) and b = G(n), resulting in c = F(n)*(3G(n)+1). This establishes a clear relationship among the variables in the equation.

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danieldf
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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:
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Sorry.. I didn't explain before.
 
danieldf said:
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))" ?
 
I mean a solutions in one variable. Like (2n, n²-1,n²+1) is a solutioin for x²+y²=z²
 
danieldf said:
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.
 
Last edited:

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