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 anoddnumber. 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