Let's say I have a set of non-negative integers $a_1,..,a_n$ and a number $C$ which is a non-negative constant (an integer).
Consider an equation
$x_1\cdot a_1 + x_2\cdot a_2 + ... + x_n\cdot a_n - C = 0$
where $x_1,...,x_n$ are unknown non-negative integers. I have to say whether a solution to this equation exists, and when does it exist and when does it not exist.
I'd really appreciate anyone's help I've been struggling with this one for quite a while.
Well so far i haven't made a good progress, i'm going to sleep and see you all in the morning.So far i got two conclusion. 1.) if the number C is not divisible by the gcd of the set than there certainly is no solution 2.)If C is divisble by gcd, If we divide all the numbers by the gcd than it becomes Frobenius coin problem.I'm now looking into upper bounds for FCP.See you all in the morning.