The generalised Collatz map f(n) = n/2 if n even, (3n+1)/2 if n odd (the 'shortcut' form) generates cycles on ℤ\{0}. Known cycles for positive integers: {1,4,2}. For negative: {-1,-2} and {-5,-14,-7,-20,-10}. Question: are these ALL cycles across all integers?
Lagarias's 1985 survey catalogued known results and noted the negative-integer extension as equally intractable. Belaga and Mignotte identified structural parallels with the positive case via p-adic analysis.
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