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Bangladesh Mathematical Olympiad 2020 Final

Source: BdMO 2020 Final Primary Category Problem 5

August 30, 2020
floor functionalgebra

Problem Statement

For a positive real number [x] [x] be its integer part. For example, [2.711]=2,[7]=7,[6.9]=6[2.711] = 2, [7] = 7, [6.9] = 6. zz is the maximum real number such that [5z\frac{5}{z}] + [6z\frac{6}{z}] = 7. Find the value of20z 20z.
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