Thus, for the numerators and , the question of how many terms are needed in an Egyptian fraction is completely settled, and fractions of the form are the first case in which the worst-case length of an expansion remains unknown. The greedy algorithm produces expansions of length two, three, or four depending on the value of modulo ; when is congruent to modulo , the greedy algorithm produces four-term expansions. Therefore, the worst-case length of an Egyptian fraction of must be either three or four. The Erdős–Straus conjecture states that, in this case, as in the case for the numerator , the maximum number of terms in an expansion is three.