Thread: If n squared is a multiple of 3...

If n squared is a multiple of 3 must n be a multiple of 3?

My approach was to assume n is not a multiple of three and so is of the form 3k+1, 3k+2, then squaring shows that n squared is not a multiple of three, but I am just not sure if this establishes the converse, does it?

Originally Posted by berachia

...must n be a multiple of 3?

My approach was to assume n is not a multiple of three and so is of the form 3k+1, 3k+2, then squaring shows that n squared is not a multiple of three, but I am just not sure if this establishes the converse, does it?

You actually proved the contrapositive, which is equivalent to what you were asked to prove in the first place.

Try proving a more general result - if p|ab => p|a OR p|b. Where p is prime and a,b are any integers.
Above will follow directly from this.