perplexus.info :: Numbers : Sum of Ratios is an Integer

Sum of Ratios is an Integer (Posted on 2024-01-25)

Determine the total number of pairs of positive integers (a,b) that satisfy both the following conditions:

(I) GCD(a, b)=1
(II) a/b + 14b/9a is an integer.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Repeat!

Comment 2 of 2 |

I thought this puzzle seemed familiar with the 14/9 ratio. It wasn't until today that I found its earlier occurrence; where I had already solved it with a number-theory approach:

Fraction Sum Satisfaction

http://perplexus.info/show.php?pid=9064

Posted by Brian Smith on 2024-01-25 23:07:04

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