Please help with exam prep! - Proofs

1. Some natural numbers can be expressed as a difference of two squares, but others cannot. For example, 12=4^2 - 2^2, but it is impossible to write 10 as a difference of two squares. Find a way to determine whether or not a given natural number can be expressed as the difference of two perfect squares.

2. In rectangle ABCD, M is the midpoint of side AD and N is the midpoint of side DC. Segments AN and CM intersect at E

a) Prove that <AEM=<MBN

b)Determine how the angles in part a are related to the length: width ratio of the rectangle.

3. A sequence is defined by the equation below:

a) Prove that every term of the sequence is less than 3.

b) Prove that every term of the sequence is greater than the preceding term.

Any help you can give me on any/all of these questions would be great, thanks.