9514 1404 393
Answer:
(2, 3, 5) or (1, 1, n) for n ≥ 1
Step-by-step explanation:
For some a, b, c, you want to show that ...
(ab -1)/c is a whole number
(ac -1)/b is a whole number
(bc -1)/a is a whole number
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A search of triples with numbers in the range of 1 to 100 gave these results:
(1, 1, n) . . . for any n ≥ 1
(2, 3, 5) . . . . apparently, the only non-trivial solution
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Further comment
We can show that if you postulate the triple is (2, x, 2x-1), then the only non-trivial value for x is 3. This gives (2, 3, 5) as above.
This triple requires ...
(2(2x -1) -1)/x = integer = (4x -3)/x = 4 -3/x
In order for 3/x to be an integer, we must have x=1 or 3. For x=1, the triple is (2, 1, 1). For x=3, the triple is (2, 3, 5).
