The greedy algorithm for Egyptian fractions finds a solution in three or fewer terms whenever "n" is not 1 or 17 (mod 24), and the "n" ≡ 17 (mod 24) case is covered by the 2 (mod 3) relation, so the only values of "n" for which these two methods do not find expansions in three or fewer terms are those congruent to 1 (mod 24).
navkljub temu so se modularne enakosti pokazala za zelo pomembno orodje pri raziskovanju domneve.