What an innocently looking equation.(adsbygoogle = window.adsbygoogle || []).push({});

If we allow negative integers, a=4, b=-1, c=11 is a solution.

Do some tricks with divisibility?

Solve for a?

Brute force with the computer?

It won't help. There are solutions, but the smallest solution has 80 digits.

What happens if we replace 4 by other integers?

a/(b+c)+b/(a+c)+c/(a+b)=178?

There are integer solutions, but the smallest one has nearly 400 million digits.

A great example how simple looking problems can have very complicated solutions.

Paper: An unusual cubic representation problem (PDF)

Here is a discussion

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# A Find positive integer solutions to a/(b+c)+b/(a+c)+c/(a+b)=4

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