In order to work with Egyptian fractions, we need to use the following table about the doubling of Egyptian fractions:

2/3 = 1/2 + 1/6 2/53 = 1/30 + 1/318 + 1/795
2/5 = 1/3 + 1/15 2/55 = 1/30 + 1/330
2/7 = 1/4 + 1/28 2/57 = 1/38 + 1/114
2/9 = 1/6 + 1/18 2/59 = 1/36 + 1/236 + 1/531
2/11 = 1/6 + 1/66 2/61 = 1/40 + 1/244 + 1/488 + 1/610
2/13 = 1/8 + 1/52 + 1/104 2/63 = 1/42 + 1/126
2/15 = 1/10 + 1/30 2/65 = 1/39 + 1/195
2/17 = 1/12 + 1/51 + 1/68 2/67 = 1/40 + 1/335 + 1/536
2/19 = 1/12 + 1/76 + 1/114 2/69 = 1/46 + 1/138
2/21 = 1/14 + 1/42 2/71 = 1/40 + 1/568 + 1/710
2/23 = 1/12 + 1/276 2/73 = 1/60 + 1/219 + 1/292 + 1/365
2/25 = 1/15 + 1/75 2/75 = 1/50 + 1/150
2/27 = 1/18 + 1/54 2/77 = 1/44 + 1/308
2/29 = 1/24 + 1/58 + 1/174 + 1/232 2/79 = 1/60 + 1/237 + 1/316 + 1/790
2/31 = 1/20 + 1/124 + 1/155 2/81 = 1/54 + 1/162
2/33 = 1/22 + 1/66 2/83 = 1/60 + 1/332 + 1/415 + 1/498
2/35 = 1/25 + 1/30 + 1/42 2/85 = 1/51 + 1/255
2/37 = 1/24 + 1/111 + 1/296 2/87 = 1/58 + 1/174
2/39 = 1/26 + 1/78 2/89 = 1/60 + 1/356 + 1/534 + 1/890
2/41 = 1/24 + 1/246 + 1/328 2/91 = 1/70 + 1/130
2/43 = 1/42 + 1/86 + 1/129 + 1/301 2/93 = 1/62 + 1/186
2/45 = 1/30 + 1/90 2/95 = 1/60 + 1/380 + 1/570
2/47 = 1/30 + 1/141 + 1/470 2/97 = 1/56 + 1/679 + 1/776
2/49 = 1/28 + 1/196 2/99 = 1/66 + 1/198
2/51 = 1/34 + 1/102 2/101 = 1/101 + 1/202 + 1/303 + 1/606
2
n
table

This is the famous "Rhind Mathematical papyrus 2/n table". There are two features in this table:

1. All Egyptian fractions in each sum are different. For example, 2/5 is written as 1/3 + 1/15
    instead of 1/5 + 1/5 .

2. There are at most four terms in each sum.

Discussion 1.2.

Can 2/n always be written as a sum of different Egyptian fractions?