What is the arithmetic nature of the fourth super-root of two?
TheoremDB P11360 · number theory
Inferred from the community field; finer classification has not been reviewed.
Problem statement
Let x be the unique real number in (1,2) satisfying the right-associated equation =2. Is x rational, algebraic irrational, or transcendental? Equivalently for the first two possibilities, does its simple continued fraction terminate or become eventually periodic?
Lean 4
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Background
Additional formulation recorded by the source
Classify the unique x in (1,2) with x^(x^(x^x))=2 as an element of Q, of algebraic closure(Q) minus Q, or of R minus algebraic closure(Q).
Progress & source assessment
Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.
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