Re: Three rational triples

On Wed, 18 Sep 2024 22:39:45 +0000, Keith F. Lynch wrote:

Keith F. Lynch <kfl@KeithLynch.net> wrote:

I discovered that these three sets of three positive rationals have
an interesting property in common:

>

9/2, 4/3, 7/6
49/15, 25/21, 54/35
49/2, 4/7, 27/14

>

If nobody figures it out, I will provide the answer in a week.

>
Since it's been more than a week, and nobody has figured it out:
>
Each of them has a sum that's equal to its product and is an integer.

              i think  one person said  exactly that.
       Is it easy to find them?
How about 2 numbers
           2+2 = 2*2
           1+x = 1*x  ------- No sol.
           3+x = 3*x  -------  easy to solve.
           A+x = A*x  -------  all  easy to solve.

>
For instance 9/2 + 4/3 + 7/6 = 7 and 9/2 x 4/3 x 7/6 = 7.
>
Here are some more triples with this same unusual property:
>
121/42, 637/66, 36/77
81/5, 50/9, 11/45
625/18, 81/50, 148/225
289/15, 950/51, 9/85
49/3, 207/7, 2/21
450/13, 169/15, 23/195
25/2, 252/5, 1/10
81/2, 292/9, 1/18
242/5, 325/11, 3/55
121/2, 92/11, 3/22
625/21, 4214/75, 81/1575
676/7, 49/26, 99/182
245/3, 198/7, 1/21
343/3, 81/7, 2/21
578/5, 175/17, 9/85
529/3, 126/23, 13/69
289/2, 756/17, 1/34
525/2, 52/5, 1/10