Even if the generalized conjecture is false for any fixed value of , then the number of fractions with in the range from to that do not have three-term expansions must grow only sublinearly as a function of . In particular, if the Erdős–Straus conjecture itself (the case ) is false, then the number of counterexamples grows only sublinearly. Even more strongly, for any fixed , only a sublinear number of values of need more than two terms in their Egyptian fraction expansions. The generalized version of the conjecture is equivalent to the statement that the number of unexpandable fractions is not just sublinear but bounded.