Solution 2: Use Linear Algebra Eigenvalue equation: A.X = λ.X
A =S(x)= where x = coconuts
Since each iteration of the transformation caused the coconut status ‘unchanged’, which means λ = 1 (see remark below)
x = – 4
Also by recursive, after the fifth monkey: =
Minimum positive x= – 4 mod ( )= = 3,121 [QED]
Note: The meaning of eigenvalue λ in linear transformation is the change by a scalar of λ factor (lengthening or shortening by λ) after the transformation. Here
λ = 1 because “before” and “after” (transformation A) is the SAME status (“divide coconuts by 5 and left 1”).