Hello again ^^
a direct proof
This would be "if x is an even number, prove that x² is an even number", using known facts.
Hint : use x=2k.
an indirect proof
This would be "if x² is an odd number, then x is an odd number".
a proof by contradiction
If x is an even number, let's suppose that x² is an odd number. Then, get to a contradiction
I'm sorry I can't give you any book references for it, as I don't know anything about American or English litterature