Statement: "All primes can be written as the sum of two squares"...

Is this true? Can you explain why?

Extension: Can all primes be written as the sum of three squares?

How many squares would you need to express all the whole numbers?

Statement: "All primes can be made by subtracting one square from another"...

Is this true?

ps Below is a print of a page from Oliver Byrne's book 'The Elements of Euclid' which has recently been reprinted; I bought one for a prize for a year 12 student last week!  I think I am going to ask students to recreate some of these proofs as posters!!