The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
The problem of finding all algebraic values of α ∈ [−1, 1] when arccos α, arcsin α and arctan α are rational multiples of π is solved. The values of such α of degree less than five are explicitly determined.
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