Find-the-number-of-rational-numbers-r-0-lt-r-lt-1-such-that-when-r-is-written-as-fraction-in-lowest-term-The-numerator-and-demominator-have-a-sum-of-1000-

Question Number 110783 by Aina Samuel Temidayo last updated on 30/Aug/20

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{rational}\:\mathrm{numbers} \\ $$$$\mathrm{r},\:\mathrm{0}<\mathrm{r}<\mathrm{1},\:\mathrm{such}\:\mathrm{that}\:\mathrm{when}\:\mathrm{r}\:\mathrm{is}\:\mathrm{written} \\ $$$$\mathrm{as}\:\mathrm{fraction}\:\mathrm{in}\:\mathrm{lowest}\:\mathrm{term}.\:\mathrm{The} \\ $$$$\mathrm{numerator}\:\mathrm{and}\:\mathrm{demominator}\:\mathrm{have}\:\mathrm{a} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{1000}. \\ $$

Commented by mr W last updated on 30/Aug/20

$$\mathrm{200} \\ $$

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

$$\mathrm{Thanks}. \\ $$

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