Is it possible to solve an equation:
a*x+b*y+....+c*z-n = 0
where {a, b,..,c, n} are natural numbers and {X, Y,...,Z} are different sets of natural numbers? Is it possible to find minima if there is no solution? Please tell me, which branch of mathematics these equations belong to (if any)?
Thanks in advance
These look like System of linear equations. However, you usually require $N$ sets of these equations if there are $N$ unknowns in order to solve them.