i know you didn't ask but as long as i'm here and there are impressionable minds around:
this is only true if you're looking for the One True Solution to a system of equations like this. There are infinitely many (I think? I didn't check but there are a lot) solutions to this equation, it's just that very, very, very few of them are ONLY integers. that's where the difficulty comes from
Actually I think there are no solutions to this particular equation. That'll take a little more than some algebra to prove though.
But otherwise, yes if you want descrete values you need the same number of equations as variables. Otherwise you can only solve for certain variables as a function of the other variable and get infinite solutions.
You need at least as many equations as variables...
Laughs in PDEs
Cries in Topology
i know you didn't ask but as long as i'm here and there are impressionable minds around: this is only true if you're looking for the One True Solution to a system of equations like this. There are infinitely many (I think? I didn't check but there are a lot) solutions to this equation, it's just that very, very, very few of them are ONLY integers. that's where the difficulty comes from
Actually I think there are no solutions to this particular equation. That'll take a little more than some algebra to prove though.
But otherwise, yes if you want descrete values you need the same number of equations as variables. Otherwise you can only solve for certain variables as a function of the other variable and get infinite solutions.