Find me and minimize me

Number Theory Level 4

Let A A and B B be positive integers such that 43 197 < A B < 17 77 . \dfrac {43}{197} < \dfrac AB < \dfrac{17}{77}.

Find the minimum possible value of B B .


The answer is 32.

Gauri shankar Mishra by Gauri shankar Mishra , 21, India

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1 solution

Vinod Kumar
Jul 15, 2018

Solve diophantine equation 197x-43y>0, 17y-77x>0, using wolfram alpha. You get (x/y) as (7/32), (9/41), (11/50), (13/59), (15/68), (19/87) and (31/142) as possible answers. Choosing lowest as (7/32) gives 32 as the answer.

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