Problem

Source: 2024 CTST P12

Tags: number theory, 2024 CTST



Given positive odd number $m$ and integer ${a}.$ Proof: For any real number $c,$ $$\#\left\{x\in\mathbb Z\cap [c,c+\sqrt m]\mid x^2\equiv a\pmod m\right\}\le 2+\log_2m.$$Proposed by Yinghua Ai