1. Exercise 1.4.2.

2. True or False? Every integer $n>2$ occurs in some Pythagorean Triple. (Justify your answer.)

3. Explain why there are only finitely many distinct Pythagorean Triples $(a,b,c)$ with $a=100$.

1. Give a geometric proof that $\sqrt{3}$ is irrational. (Hint: It might be easier to show that $1+\sqrt{3}$ is irrational, then deduce that $\sqrt{3}$ is also irrational.)

2. Use the Euclidean algorithm to find an integral solution to $270x+168y = 6$.

3. What is the height of a regular tetrahedron of side length 1?