Problem 1909. Two fractions, one sum

Created by James

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Given a positive number x, write a MATLAB script that will tell you how many ways that the reciprocal of that number can be written as a sum of two reciprocals of integers. For example, 1/10 can be written as:

1/11 + 1/110
1/12 + 1/60
1/14 + 1/35
1/15 + 1/30
1/20 + 1/20

The order of the fractions does not matter, so 1/11+1/110 is the same as 1/110+1/11. Therefore, two_fractions(10)=5. You do not need to output the fraction pairs themselves, only the total number of sums. Good luck!

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Last Solution submitted on Jul 29, 2025

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Nick on 3 Oct 2013

Although people have solved this already. I'm sure that there's an error in the 7th test suite.

two_fractions(10^7) = 113;
two_fractions(10^8) = 165;

two_fractions(two_fractions(10^7) + two_fractions(10^8)) ==> two_fractions(278) = 5 ==> not 14

James on 3 Oct 2013

Nick, I see where your problem is: two_fractions(10^8) is not 165. You are running into rounding errors on some of your larger fractions.

Nick on 3 Oct 2013

Ok Thanks. I'll have a look.

J.R.! Menzinger on 21 Oct 2013

http://www.wolframalpha.com/input/?i=%28x%2By%29*5+%3D+x*y

Ramon Villamangca on 12 Oct 2021

Nice problem!

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Problem 1909. Two fractions, one sum

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Problem 1909. Two fractions, one sum

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Last 200 Solutions

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Problem Recent Solvers26

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