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Problem 33 (Integer Linear Combination Practice)
Complete the following.
- Compute the span of $3$, i.e. make a list of the elements in this set. In general, what is the span of a single integer $a$? (We know it by a different name.)
- What is $\text{span}(4,6)$? List the elements. Find a single number $a$ so that $\text{span}(a)=\text{span}(4,6)$.
- What is $\text{span}(4,5)$?
- Let $S=\{a_1,a_2,\ldots,a_k\}$ be a set of integers. Show that if $c\in \text{span}(S)$, then so is every multiple of $c$.
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