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split k sheep into [k/2] , [k/3], [k/5] sheep

Source: Portugal OPM 2003 p5

May 19, 2024
algebrafloor functionnumber theory

Problem Statement

A shepherd left, as an inheritance, to his children a flock of kk sheep, distributed as follows: the oldest received ⌊k2⌋\left\lfloor\frac{k}{2}\right\rfloor sheep, the middle one ⌊k3⌋\left\lfloor\frac{k}{3}\right\rfloor sheep and the youngest ⌊k5⌋\left\lfloor\frac{k}{5}\right\rfloor sheep. Knowing that there are no sheep left, determine all possible values for kk.
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