Find all non-empty finite sets of integers A and B with the following properties:
(i) Whenever x∈A, x+1∈B.
(ii) Whenever x∈B, x2-4∈A.
Combining the two properties, we conclude that
w
henever x∈B, (x2-3)∈B.
I tried the integers from -5 to 5, and the only finite set B that seemed to work was B = {-2, 1}. Which makes the only A = {-3,0}
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Except I seem to be wrong. I just saw Larry's solution, which I like better
Edited on June 19, 2024, 10:29 am
Semi-analytical solution (spolier)
