1. Suppose that http://stuff.daniel15.com/cgi-bin/mathtex.cgi?a,b,c,d are real numbers such that

http://stuff.daniel15.com/cgi-bin/ma...0b%5E2%20=%201

http://stuff.daniel15.com/cgi-bin/ma...0d%5E2%20=%201

http://stuff.daniel15.com/cgi-bin/mathtex.cgi?ac+bd=0

Show that

http://stuff.daniel15.com/cgi-bin/ma...0c%5E2%20=%201

http://stuff.daniel15.com/cgi-bin/ma...0d%5E2%20=%201

http://stuff.daniel15.com/cgi-bin/ma...+%20cd%20=%200

(Problem can get messy but there is an elegant and complete solution)

2. Find all integer solutions http://stuff.daniel15.com/cgi-bin/mathtex.cgi?%28n,m%29 to http://stuff.daniel15.com/cgi-bin/ma...5E2+2n+1=m%5E2

3. Find the smallest positive integer whose cube ends in 888.