MathDB

Problem 7

Part of 2019 LIMIT Category B

Problems(2)

segments intersecting outside circle

Source: LIMIT 2019 CBS1 P7

4/28/2021
AB‾\overline{AB} and CD‾\overline{CD} are segments of a circle that intersect at a point PP outside the circle. Calculate the value of xx. https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvNy9lL2RkZGQwNDViNTA1MzM5MDI0NDQ5MDEyOTZhZGUyNTEyYjgyZTNkLnBuZw==&rn=U2NyZWVuIFNob3QgMjAyMS0wNC0yOCBhdCAxMC4wMy4zMSBBTS5wbmc=
geometry
1/a+1/b=4/2019 over N

Source: LIMIT 2019 CBS2 P7

4/28/2021
Find the number of ordered pairs of positive integers for which 1a+1b=42019\frac1a+\frac1b=\frac4{2019}
Diophantine equationnumber theory