This week, we continued discussing infinite sets of numbers, bijections, and modular arithmetic (alongside Pythagorean triples).
Here are some challenge problems to consider!
- Are there natural numbers such that ? If so, find them, if not, explain why.
- Are there such that and exactly two of a,b,c are divisible by n? If so, find an example, if not, provide an argument why.
- Again let be a Pythagorean triple. Show that if is not divisible by , then neither are or .
- How many surjections are there from to ? How about surjections from to ?