This assignment is due next Thursday.

1. Pythogoras knew that there was no rational number whose square was 2, - and he didn't show that using number theory or unique factorization. Greek proofs worked with the diagonal of a unit square. Find one that does that. Be prepared to present it.

   Hint: 2 has a rational square root if and only if there is an isosceles right triangle with integer sides.

   You can use the internet to find a proof - but you'll have to understand it to present it at the board without notes.

2. Silverman 20.1. Easy - it's just computation. Don't bother turning it in, but use the data.

3. Silverman 20.2.

4. Silverman 20.3. For those of you who know some Abstract Algebra - why is part (b) really about the three cosets of a subgroup of Z_19^*?