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Least fraction closest to 31/17

Source: LIMIT 2020 Cat 1 Obj P12

May 2, 2020
number theorylimit

Problem Statement

qq is the smallest rational number having the following properties:
(i) q>3117q>\frac{31}{17}
(ii) when qq is written in its reduced form ab\frac{a}{b}, then b<17b<17
As in part (ii) above, find a+ba+b.
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