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
a solution by xdog)
In general, let a = c + k.
Then b = a^2 / k - a.
So a + b = a^2 / k.
Yours is the special case when k = 1. By observation, k must be a square number to make the equation work (and thus a + b is always square). But my math is too rusty to prove it at the moment.
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Posted by tomarken
on 2020-03-06 10:03:30 |
re: a solution
