Cory Taylor
2003-03-06 05:08:36 |
perfect squares
I want to confirm something that I think to be true. Does zero count as a perfect square, or does the definition exclude this trivial case? |
fwaff
2003-03-06 05:28:37 |
Re: perfect squares
My understanding is that a perfect square is essentially the square of an integer. Since zero is an integer, then presumably it's square is perfect. |
Gamer
2003-04-06 05:16:06 |
Re: perfect squares
I agree with fwaff, I always remember this because the first differences between them are the odd numbers: 1 3 5 7, and without zero, you wouldn't have the 1. |
Cory Taylor
2003-12-02 14:45:27 |
Re: perfect squares
Another dumb question - sorry its not related to the forum title, but since I've got one here already I figured I'd continue my trend...
I don't recall the rigorous definition of a "prime" number, just the everyday definition that a prime is a number with only two factors - one and itself. Now this serves as a very adequate definition, but,
what about -1? Does the rigorous definition exclude this or is this in fact a prime number? |
SilverKnight
2003-12-02 14:47:17 |
Re: perfect squares
the definition requires it (and the factors) be positive...
otherwise 3 is evenly divisible by -1, 1, -3, and 3. |
Victor Zapana
2003-12-02 20:25:18 |
Re: perfect squares
and techincally thats why 1 can't be prime either. if it included negative factors, 1 would have 1 and -1, making it prime. However, prime numbers don't include negative, that's why 1 isn't prime. |
DJ
2003-12-02 22:42:15 |
Re: perfect squares
Actually, if we included negative numbers, -1 and 1 would be the only numbers with exactly two integral factors, while other 'normal' primes would each have four. Every integer is considered a multiple of 1 and a factor of 0.
The 'rigorous' definition is simple enough: a prime number is an integer with exactly two positive integral factors. |
Victor Zapana
2003-12-02 22:50:56 |
Re: perfect squares
i agree. |
