# Lattice points on a circle.

1. Nov 4, 2012

### funcalys

Does any circle having irrational radius have no lattice points on its boundary ?
Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ?
*The centres of these circles are all (0,0) *

Last edited: Nov 4, 2012
2. Nov 4, 2012

### Edgardo

What do you mean by lattice points? Points (x,y) where x and y are integers?

The circle with radius 1/sqrt(2) comes to my mind.

3. Nov 4, 2012

### funcalys

Thanks, but the equation x^2 + y^2 =1/2 seems to have no integer solution...

4. Nov 4, 2012

### pwsnafu

Isn't that what you asked for?

5. Nov 4, 2012

### funcalys

Ah, my bad :tongue:, I meant to ask if EVERY circle having irrational radius have no lattice points on its boundary, not an example .

6. Nov 4, 2012

### Petek

The boundaries of many circles having an irrational radius contain lattices points. For example, can you find lattice points on a circle of radius √2? What about one with radius √5?

7. Nov 4, 2012

### funcalys

Thanks, I didn't think thoroughly before posting this silly question, sorry.