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Two of them

Source: UMD 2023 I #15

October 23, 2023

UMDalgebra

Problem Statement

What is the least positive integer

m

such that the following is true?
Given

\it m

integers between

\mathrm a. ~ 10\qquad \mathrm b.~11\qquad \mathrm c. ~12 \qquad \mathrm d. ~13 \qquad \mathrm e. ~1415

and

\it{2023},

inclusive, there must exist two of them

\it a, b

such that

1 < \frac ab \le 2.

\mathrm a. ~ 10\qquad \mathrm b.~11\qquad \mathrm c. ~12 \qquad \mathrm d. ~13 \qquad \mathrm e. ~1415

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