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...)?
(In reply to re: Possible solution, first posting
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