# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a260819 Showing 1-1 of 1 %I A260819 #32 Sep 09 2017 23:27:44 %S A260819 2,3,7,42,2,3,8,24,2,3,9,18,2,3,10,15,2,3,12,12,2,4,5,20,2,4,6,12,2,4, %T A260819 8,8,2,5,5,10,2,6,6,6,3,3,4,12,3,3,6,6,3,4,4,6,4,4,4,4 %N A260819 Positive integer solutions [a',b',c',d'] of the equation 1/a + 1/b + 1/c + 1/d = 1, for a <= b <= c <= d, lexicographically sorted. %C A260819 There are only 14 positive integer solutions for 1/a + 1/b + 1/c + 1/d = 1. %D A260819 W. SierpiÅ„ski, 250 problems in elementary number theory, Elsevier Science Ltd, pages 14 and 83-85. %H A260819 Eric Weisstein's World of Mathematics, Egyptian Fraction %H A260819 Index entries for sequences related to Egyptian fractions %e A260819 The 2nd row is [2,3,8,24] and represents the solution 1/2 + 1/3 + 1/8 + 1/24 = 1. %e A260819 List of all the solutions: %e A260819 1/2 + 1/3 + 1/7 + 1/42 = 1 %e A260819 1/2 + 1/3 + 1/8 + 1/24 = 1 %e A260819 1/2 + 1/3 + 1/9 + 1/18 = 1 %e A260819 1/2 + 1/3 + 1/10 + 1/15 = 1 %e A260819 1/2 + 1/3 + 1/12 + 1/12 = 1 %e A260819 1/2 + 1/4 + 1/5 + 1/20 = 1 %e A260819 1/2 + 1/4 + 1/6 + 1/12 = 1 %e A260819 1/2 + 1/4 + 1/8 + 1/8 = 1 %e A260819 1/2 + 1/5 + 1/5 + 1/10 = 1 %e A260819 1/2 + 1/6 + 1/6 + 1/6 = 1 %e A260819 1/3 + 1/3 + 1/4 + 1/12 = 1 %e A260819 1/3 + 1/3 + 1/6 + 1/6 = 1 %e A260819 1/3 + 1/4 + 1/4 + 1/6 = 1 %e A260819 1/4 + 1/4 + 1/4 + 1/4 = 1 %Y A260819 Cf. A229941. %K A260819 easy,full,fini,nonn,tabf %O A260819 1,1 %A A260819 _Marco RipÃ _, Jul 31 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE