Dumir, V. C. ; HansGill, R. J. (1977) On a conjecture of Mahler Bulletin of the Australian Mathematical Society, 16 (01). pp. 125129. ISSN 17551633

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Abstract
Let R be the field of real numbers. For a in R, let α be the distance of a from the nearest integer. The following conjecture of Kurt Mahler [Bull. Austral. Math. Soc. 14 (1976), 463465] is proved. Let m, n be two positive integers n ≥ 2m. Let S be a finite or infinite set of positive integers with the following properties: (Q_{1}) S contains the integers m, m+1, …, nm; (Q_{2}) every element of S satisfies θ/n ≥ m/n then sup infεα m/n. αεR eεS.
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