# Basic Number Theory

• November 2nd 2009, 05:07 AM
Aquafina
Basic Number Theory
1. Is there such number N that 7 divided N^2=3?

Isnt it just root of 7/3?

2. x^2 + y^2 = z^2. Prove xyz is a multiple of 60

Not sure what to do here, and where to get the xyz term from
• November 2nd 2009, 07:16 PM
jmedsy
1)

I assume you mean 7 divided by n^2 = 3

If you're dealing with divisibility in number theory, I think the question may be asking if there is an integer which divides 7 giving the quotient 3. This would mean that 7 would have 3 as a factor. 7, being prime, has no factors.

However the root of 7/3 does does yield a quotient of 3. The number does exist (root of 7/3), but it is not an integer.
• November 2nd 2009, 08:55 PM
alexmahone
Quote:

Originally Posted by Aquafina
1. Is there such number N that 7 divided N^2=3?

Isnt it just root of 7/3?

2. x^2 + y^2 = z^2. Prove xyz is a multiple of 60

Not sure what to do here, and where to get the xyz term from

2. $x^2+y^2=z^2$

The solution set is $(x, y, z)=(3k, 4k, 5k)$. $xyz=60k^3$. Thus xyz is a multiple of 60.
• November 2nd 2009, 09:21 PM
DavidEriksson
Quote:

Originally Posted by alexmahone
2. $x^2+y^2=z^2$

The solution set is $(x, y, z)=(3k, 4k, 5k)$. $xyz=60k^3$. Thus xyz is a multiple of 60.

so what about the set (5,12,13)?

You've got to try the following:
Prove that one of the numbers are divisble by 5,
prove that one of them is divisible by 3
and prove that one of them i divisible by 4.

These statements are true and should not be to hard to prove.