Discussion Overview
The discussion centers around the presence of lattice points on the boundary of circles with irrational radii. Participants explore whether circles with irrational radii can have lattice points and seek to determine the number of such points for given circles centered at the origin.
Discussion Character
- Exploratory, Debate/contested, Conceptual clarification
Main Points Raised
- One participant questions if any circle with an irrational radius has no lattice points on its boundary.
- Another participant clarifies the definition of lattice points as points where both coordinates are integers.
- A participant notes that the equation for a specific circle (radius 1/sqrt(2)) does not yield integer solutions.
- There is a correction where a participant expresses a desire to ask if every circle with an irrational radius has no lattice points, rather than just providing an example.
- Some participants suggest that circles with irrational radii, such as those with radii √2 and √5, may indeed contain lattice points.
- One participant acknowledges a lack of thorough consideration in their initial question about lattice points.
Areas of Agreement / Disagreement
Participants do not reach a consensus; there are competing views regarding the presence of lattice points on circles with irrational radii.
Contextual Notes
The discussion does not resolve the mathematical conditions under which lattice points may or may not exist on the boundaries of circles with irrational radii.
, I meant to ask if EVERY circle having irrational radius have no lattice points on its boundary, not an example 
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