- Prove that every odd prime number can be written as a difference of two squares.
- Prove also that this presentation is unique.
- Is such presentation possible if p is just an odd natural number?
- Can 2 be represented this way?
\3. Yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. For example, $57=11^2-8^2=29^2-28^2$.
\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.
Can I get some help in proving questions 1 and 2?