Let-n-amp-k-be-positive-integers-and-let-S-be-a-set-of-n-points-in-The-plane-such-that-For-any-point-P-of-S-there-are-at-least-K-points-of-S-Equidistant-from-p-Prove-that-k-lt-1-2-2n-

Question Number 193853 by York12 last updated on 21/Jun/23

L e t n & k b e p o s i t i v e i n t e g e r s a n d l e t

S b e a s e t o f n p o i n t s i n T h e p l a n e s u c h t h a t :

F o r a n y p o i n t P o f S t h e r e a r e a t l e a s t K p o i n t s o f S E q u i d i s t a n t f r o m p

P r o v e t h a t k < \frac{1}{2} + \sqrt{2 n}