Lattice points on a circle.

[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) *

 

[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.

 

[funcalys]

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

 

[pwsnafu]

Isn't that what you asked for?

 

[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 .

 

[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?

 

[funcalys]

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?

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