### Is 1 a square number?

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closed account (EwCjE3v7)
Well my teacher said it's not counted but 1 * 1 = 1.
Wikipedia and OEIS agrees with you: http://oeis.org/A000290
Yup it is.

Like you said 12 = 1 hence it is a square number. 0 is also a square number.
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closed account (EwCjE3v7)
Thank you guys, I can prove my teacher wrong for once(I was right all along :))
You sure she didn't mean prime? 'Cause you'll often have "all primes excluding one" or just not include one when dealing with primes.
1 is not considered prime in mathematics. Here is a neat explanation by Dr. James Grime: https://www.youtube.com/watch?v=IQofiPqhJ_s
Well there you go.
closed account (EwCjE3v7)
Yea I'm sure, Ibtold her today about it anyway. And thanks for that Ibwill check it out now
You dont need a mathematical explanation... Just to use the correct definition.
A prime number has exactly 2 integer factors.

With that definition 1 is ruled out as it's only got 1 factor which is 1.

As for the rest 1 is a square, triangle, cubic, quartic, etc number... Same with 0 except for the triangle.
http://en.wikipedia.org/wiki/Triangular_number
0 is triangular.

> A prime number has exactly 2 integer factors.
> With that definition 1 is ruled out as it's only got 1 factor which is 1.
1 may be divided by 1, or by -1
it has 2 integer factors

> Just to use the correct definition.
A natural number greater or equal than 2 is prime if...

By the way, if you allow complex factors then 13 is not prime
13 = (3+j2) (3-j2)
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@ ne555: Since when can a negative number be a factor? Or is this a different use of the word "factor" then for example: "Factors of '12' are '2' and '3' "?

EDIT: I'm not trying to butt heads by the way, this is a legitimate question on my part.

EDIT 2: Never mind, I'm so used to seeing complex numbers written with the variable on the right hand side of the mutiplicand that it took me a minute to realize that it's just a binomial you wrote and not something more complex. I'm chalking this one up to my American education.
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Dividing by -1 just makes a positive number negative or vice-versa.

The proper definition of a prime is that it has two positive integer factors, itself and one.

You can get completely different primes in complex numbers and also if you start using other counting systems.
@ne555: Why do you put the j before the coefficient? Is this some convention I was taught wrong/not taught about?
Well, j is just a number denoting sqrt(-1). You can write 2×3, 3×2 or 2×e, e×2, 5×j, j×5 and it will be correct. It is just your preference.
http://en.wikipedia.org/wiki/Complex_number#Notation
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I know, but I am used to the convention that letter values, whether they are const or variable, go after coefficients. I didn't know if my understand of this convention was incorrect.
Also, it is worth stating that any prime number that can be represented as the sum of two squares has got complex factors with integer coefficients.
Mathematically:
If p^2+q^2 (where p and q are integers) is prime the it has complex factors:
(p+jq)(p-jq)
and
(q+jp)(q-jp)

At least that is what I understand to be true.
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Er, I know some math, but why are we using j for √(-1) instead of i?

And, while integer multiplication is commutative, it is standard to write the coefficient first, so that (3+j2) is universally understood when written (3+2i).
j is often uses instead of i in physics because of name clashing here. Wiki link I provided before mentions it.
In electronics they use j instead of i.
So they don't mix it up with current.
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Well then ne555, I'll correct my definition to say that a prime is a number that contains only one pair of positive factors.

Even though you're just being picky because I'm sure everyone knew exactly what I meant.
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