Try to solve this problem by a method which is different from the solution to "Harmonic Integers" problem.

Given that, a, b, and c are all positive integers so that a < b < c, and 1/a, 1/b, and 1/c are in Arithmetic Progression, can a + b be equal to c?

See The Solution	Submitted by K Sengupta
Rating: 4.5000 (2 votes)

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re: One Approach

| Comment 2 of 3 |

(In reply to One Approach by Richard)

Once we have 2 a^2 = b^2, there are, as Richard correctly observes, various ways forward to prove this has no solution in positive integers.

The simplest I think is to note that it implies

the irrational sqrt(2) = b/a rational.

Posted by goFish on 2006-02-21 16:04:01