The only solutions found by brute force are:
p q r
3 2 7
5 3 5
The following might be useful in pointing towards a proof that these are the only solutions.
Here is a partial list of prime values for r and the second expression in the equation:
r 4/(r+1)
2, '4/3'
5, '2/3' p/q = 5/3
7, '1/2' p/q = 3/2
11, '1/3'
13, '2/7'
17, '2/9'
19, '1/5'
23, '1/6'
29, '2/15'
31, '1/8'
37, '2/19'
41, '2/21'
43, '1/11'
47, '1/12'
53, '2/27'
59, '1/15'
61, '2/31'
67, '1/17'
71, '1/18'
73, '2/37'
79, '1/20'
83, '1/21'
89, '2/45'
97, '2/49'
In every case except for the two solutions, adding 1 to the fraction in quotes has at least one of the integers being a non prime.
But this is not a formal proof.
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Posted by Larry
on 2024-04-05 07:19:54 |
I found ...
