P/Q is a fraction with the smallest positive integer denominator that satisfy the undernoted inequality:
386 P 35
----- < --- < ----
2019 Q 183
where P is also a positive integer.
Determine the minimum value of P+Q
We had a similar problem to this with
Minimizing the Denominator. I eventually solved it analytically with continued fractions.
Continued fraction representations for the two bounds are 386/2019 = [0;5,4,2,1,29] and 35/183 = [0;5,4,2,1,2].
Then the fraction with the smallest denominator between 386/2019 and 35/183 would be [0;5,4,2,1,3] = 48/251. Then the minimum P+Q = 299.
Continued Fractions
