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Adri

International Zhautykov Olympiad 2016, Hari Kedua: No 6

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Bilangan asli $q$ disebut pecahan lancar dari bilangan real $\alpha$ apabila ketaksamaan $\left| \alpha- \frac{p}{q}\right| < \frac{1}{10q}$ terpenuhi untuk suatu $p$ bilangan bulat. Buktikan bahwa apabila bilangan irasional $\alpha$ dan $\beta$ mempunyai himpunan pecahan lancar yang sama maka $\alpha+\beta$ atau $\alpha-\beta$ merupakan bilangan bulat.

Edited by Adri

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