perplexus.info :: Numbers : co-prime unit fractions

co-prime unit fractions (Posted on 2020-03-06)

There are 3 positive integers a, b, c such that 1/c=1/a+1/b. If the greatest common divisor of a, b, c is 1, then what type of number must a+b be(e.g square number, cube number, triangular number...)?

No Solution Yet Submitted by Danish Ahmed Khan

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a solution

| Comment 1 of 7

One solution meeting the problem constraints is a=c+1 and b=c(c+1).

Then a+b=(c+1)^2.

Posted by xdog on 2020-03-06 09:38:41

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