The Erdős-Straus Conjecture

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Abstract

The conjecture states that for every n>1, there exist positive integers a, b and c satisfying 4/n=1/a+1/b+1/c.
In this Knol we give verifying examples for n<127.

4/2 = 1/1 + 1/2 + 1/2
4/3 = 1/2 + 1/2 + 1/3
4/4 = 1/3 + 1/3 + 1/3
4/5 = 1/2 + 1/10 + 1/5
4/6 = 1/4 + 1/4 + 1/6
4/7 = 1/4 + 1/4 + 1/14
4/8 = 1/6 + 1/6 + 1/6
4/9 = 1/6 + 1/6 + 1/9
4/10 = 1/5 + 1/10 + 1/10
4/11 = 1/6 + 1/6 + 1/33
4/12 = 1/9 + 1/9 + 1/9
4/13 = 1/4 + 1/52 + 1/26
4/14 = 1/7 + 1/14 + 1/14
4/15 = 1/10 + 1/12 + 1/12
4/16 = 1/12 + 1/12 + 1/12
4/17 = 1/6 + 1/102 + 1/17
4/18 = 1/12 + 1/12 + 1/18
4/19 = 1/6 + 1/38 + 1/57
4/20 = 1/15 + 1/15 + 1/15
4/21 = 1/14 + 1/14 + 1/21
4/22 = 1/11 + 1/22 + 1/22
4/23 = 1/12 + 1/12 + 1/138
4/24 = 1/18 + 1/18 + 1/18
4/25 = 1/10 + 1/25 + 1/50
4/26 = 1/13 + 1/26 + 1/26
4/27 = 1/18 + 1/18 + 1/27
4/28 = 1/21 + 1/21 + 1/21
4/29 = 1/10 + 1/29 + 1/290
4/30 = 1/20 + 1/24 + 1/24
4/31 = 1/16 + 1/16 + 1/248
4/32 = 1/24 + 1/24 + 1/24
4/33 = 1/22 + 1/22 + 1/33
4/34 = 1/17 + 1/34 + 1/34
4/35 = 1/30 + 1/30 + 1/21
4/36 = 1/27 + 1/27 + 1/27
4/37 = 1/10 + 1/185 + 1/370
4/38 = 1/19 + 1/38 + 1/38
4/39 = 1/26 + 1/26 + 1/39
4/40 = 1/30 + 1/30 + 1/30
4/41 = 1/12 + 1/123 + 1/164
4/42 = 1/30 + 1/30 + 1/35
4/43 = 1/12 + 1/172 + 1/258
4/44 = 1/33 + 1/33 + 1/33
4/45 = 1/30 + 1/30 + 1/45
4/46 = 1/23 + 1/46 + 1/46
4/47 = 1/14 + 1/94 + 1/329
4/48 = 1/36 + 1/36 + 1/36
4/49 = 1/28 + 1/28 + 1/98
4/50 = 1/25 + 1/50 + 1/50
4/51 = 1/34 + 1/34 + 1/51
4/52 = 1/39 + 1/39 + 1/39
4/53 = 1/18 + 1/53 + 1/954
4/54 = 1/36 + 1/36 + 1/54
4/55 = 1/40 + 1/40 + 1/44
4/56 = 1/42 + 1/42 + 1/42
4/57 = 1/38 + 1/38 + 1/57
4/58 = 1/29 + 1/58 + 1/58
4/59 = 1/30 + 1/30 + 1/885
4/60 = 1/45 + 1/45 + 1/45
4/61 = 1/16 + 1/488 + 1/976
4/62 = 1/31 + 1/62 + 1/62
4/63 = 1/42 + 1/42 + 1/63
4/64 = 1/48 + 1/48 + 1/48
4/65 = 1/39 + 1/52 + 1/60
4/66 = 1/44 + 1/44 + 1/66
4/67 = 1/18 + 1/402 + 1/603
4/68 = 1/51 + 1/51 + 1/51
4/69 = 1/46 + 1/46 + 1/69
4/70 = 1/60 + 1/60 + 1/42
4/71 = 1/284 + 1/355 + 1/20
4/72 = 1/54 + 1/54 + 1/54
4/73 = 1/21 + 1/146 + 1/3066
4/74 = 1/37 + 1/74 + 1/74
4/75 = 1/50 + 1/66 + 1/55
4/76 = 1/57 + 1/57 + 1/57
4/77 = 1/42 + 1/66 + 1/77
4/78 = 1/52 + 1/60 + 1/65
4/79 = 1/21 + 1/474 + 1/1106
4/80 = 1/60 + 1/60 + 1/60
4/81 = 1/54 + 1/54 + 1/81
4/82 = 1/41 + 1/82 + 1/82
4/83 = 1/70 + 1/1743 + 1/30
4/84 = 1/63 + 1/63 + 1/63
4/85 = 1/40 + 1/68 + 1/136
4/86 = 1/43 + 1/86 + 1/86
4/87 = 1/58 + 1/58 + 1/87
4/88 = 1/66 + 1/66 + 1/66
4/89 = 1/24 + 1/534 + 1/712
4/90 = 1/60 + 1/60 + 1/90
4/91 = 1/52 + 1/52 + 1/182
4/92 = 1/69 + 1/69 + 1/69
4/93 = 1/62 + 1/62 + 1/93
4/94 = 1/47 + 1/94 + 1/94
4/95 = 1/60 + 1/60 + 1/114
4/96 = 1/72 + 1/72 + 1/72
4/97 = 1/28 + 1/194 + 1/2716
4/98 = 1/49 + 1/98 + 1/98
4/99 = 1/66 + 1/66 + 1/99
4/100 = 1/75 + 1/75 + 1/75
4/101 = 1/28 + 1/404 + 1/707
4/102 = 1/68 + 1/68 + 1/102
4/103 = 1/30 + 1/206 + 1/1545
4/104 = 1/78 + 1/78 + 1/78
4/105 = 1/70 + 1/78 + 1/91
4/106 = 1/53 + 1/106 + 1/106
4/107 = 1/30 + 1/321 + 1/1070
4/108 = 1/81 + 1/81 + 1/81
4/109 = 1/30 + 1/545 + 1/654
4/110 = 1/80 + 1/80 + 1/88
4/111 = 1/74 + 1/74 + 1/111
4/112 = 1/84 + 1/84 + 1/84
4/113 = 1/30 + 1/678 + 1/1695
4/114 = 1/76 + 1/76 + 1/114
4/115 = 1/60 + 1/92 + 1/138
4/116 = 1/87 + 1/87 + 1/87
4/117 = 1/78 + 1/78 + 1/117
4/118 = 1/59 + 1/118 + 1/118
4/119 = 1/84 + 1/84 + 1/102
4/120 = 1/90 + 1/90 + 1/90
4/121 = 1/66 + 1/66 + 1/363
4/122 = 1/61 + 1/122 + 1/122
4/123 = 1/82 + 1/82 + 1/123
4/124 = 1/93 + 1/93 + 1/93
4/125 = 1/50 + 1/125 + 1/250
4/126 = 1/90 + 1/90 + 1/105