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co-prime unit fractions (Posted on 2020-03-06) Difficulty: 3 of 5
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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re(2): Possible solution, first posting | Comment 6 of 7 |
(In reply to re: Possible solution, first posting by xdog)

Your examples fit quite nicely into the second case i described, with 

x=2, y=5, k=l=7
x=2, y=11, k=l=13
x=3, y=35, k=l=38

The weakness in my argument is in the last part from wlog let y=k-x onwards, which clearly needs more thought.


Edited on March 8, 2020, 1:42 pm
  Posted by broll on 2020-03-08 13:33:48

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