MathDB
IOQM 2023-24 P-1

Source:

September 3, 2023

Problem Statement

Let nn be a positive integer such that 1≤n≤10001 \leq n \leq 1000. Let MnM_n be the number of integers in the set Xn={4n+1,4n+2,…,4n+1000}X_n=\{\sqrt{4 n+1}, \sqrt{4 n+2}, \ldots, \sqrt{4 n+1000}\}. Let a=max⁡{Mn:1≤n≤1000}, and b=min⁡{Mn:1≤n≤1000}.  a=\max \left\{M_n: 1 \leq n \leq 1000\right\} \text {, and } b=\min \left\{M_n: 1 \leq n \leq 1000\right\} \text {. } Find a−ba-b.
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