A proof is an argument used to show that something is either unambiguously true or unambiguously false.
It should be written in a concise form.
Arguments should be clear and consistant.
A proof should not start by assuming the claim is true.
A proof should have sufficient explanation of why certain steps are taken.
There should be no room for confusion in the proof.
We can use certain rules from both the lectures and textbook without additional proof.
There is no need to over-complicate a proof by including a number of mathematical systems to make it shorter.
Often negative numbers or $0$ may be an issue with your proof.
Ensure that you prove your statement is true for all numbers that it allows.
There is no clear answer to the question of which proof method should be chosen.
$$\begin{array}{c|c} \text{Claim Type}&\text{Possible Method}\\ \hline\\ \text{If/Then}&\text{Direct Proof}\\ \text{Modular Arithmetic}&\text{Cases}\\ \text{Something Exists}&\text{Construction}\\ \text{Sequences/Recursion}&\text{Induction}\\ \text{Stuck?}&\text{Try Contradiction}\\ \text{Still Stuck?}&\text{Maybe it's false, try disprove}\\ \end{array}$$