This week, we continued discussing infinite sets of numbers, bijections, and modular arithmetic (alongside Pythagorean triples).

Here are some challenge problems to consider!

  1. Are there natural numbers a, b such that \frac{a}{b} = \sqrt{2}?  If so, find them, if not, explain why.
  2. Are there a, b, c, n such that a^2+b^2=c^2 and exactly two of a,b,c are divisible by n?  If so, find an example, if not, provide an argument why.
  3. Again let a, b, c be a Pythagorean triple.  Show that if c is not divisible by 7, then neither are a or b.
  4. How many surjections are there from \mathbb{Z}_7 to \mathbb{Z}_6?  How about surjections from \mathbb{Z}_n to \mathbb{Z}_{n+1}?

 

 

One Response to SMA109: Week Three

  1. kirui cheruiyot says:

    i find this page infomative

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Some Maths Links

Vi Hart - Hyperactive videos about beautiful math concepts. Snowdecahedron - A mathematical art installation. Tau - An alternative to pi. BBC Brief History of Math - A Documentary. John Baez - A maths superhero.
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