Proposition 1. Let n, a, b and c be integers.
If a + b \equiv c \mod n, then a \equiv c - b \mod n.
Proposition 2. Let e, f and g be integers. If e|f and e|g, then e|3f + 2g.
All that is required for this homework are the proofs in paragraph form for
these two propositions. If you would like possible partial credit, you may want
to complete the following four steps for each proposition to show your work and
build up to the proofs.
1) State the definition of n|x and the definition of x \equiv y \mod n.
2) Experiment with at least four sets of values for the given list of integers
and all of the quantities listed in the relevant proposition.
3) Write notes to prepare for writing a formal proof. These notes should
include statements about the hypotheses, about what we want to prove, and
the algebra that connects what is known with the conclusion.
4) Write a formal proof of this proposition. This proof should have beginning
and end statements. It should be in paragraph form, with full sentences.
