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

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

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

Commented bymr W last updated on 30/Aug/20


$$\mathrm{200} \\ $$

Commented byAina Samuel Temidayo last updated on 03/Sep/20


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

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