Question

Set of numbers that can be formed from a linear combination

Answer 1

$\color{red}\huge\bold\star\underline\mathcal{Hey\:Mate}\star$

here is ur answer ❤❤❤❤

Step-by-step explanation:

Theorem: Let a,b be two positive integers. Then there is a finite set N of positive integers smaller than lcm(a,b) such that:

{k1a+k2b∣k1,k2∈N}={lcm(a,b)+k×gcd(a,b)∣k∈N}∪N.

I'm also interested in its generalization to any number of integers: Say a set of integers is a linear set with n periods if it can be written as:

{c0+

n

∑

i=1 ki×ci∣ki∈N}.

Then:

Theorem: Any linear set is the union of a finite set and a linear set with one period.

Thanks!✔✔✔✔