Table 2 / n of the Rhind papyrus

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Reason: This article, created by a user who has since been blocked, is essentially just a table with a few mathematical explanations. To get an article from it, one would have had to discuss the historical context in detail on the basis of the literature. But even then, the question of relevance arose: why should we single out this table and dedicate a separate article to it? Of course there is already an article Papyrus Rhind. - Hoegiro ( discussion ) 18:03, 16 Aug 2020 (CEST)

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This article refers to the first part of the Rhind papyrus , a copy by the scribe Ahmes (ancient Egyptian jꜥḥ-ms) around 1550 BC. u. At the time a source was about two hundred years older.

The following table shows the sums of fractions of with in the papyrus . ${\ displaystyle 2 / n}$ ${\ displaystyle 3 \ leq n \ leq 101}$

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

With these sums, the denominators of the (selected) original fractions are except for composite numbers , whose prime factors are respectively . When selecting (and calculation) of this unit fractions is still unresolved, that the modern methods ( Mathematica computable) single instance with four different unit fractions with a prime factor illustrated in the denominator of the last two unit fractions. ${\ displaystyle {2,3, n}}$ ${\ displaystyle \ leq n}$ ${\ displaystyle 2/101 = 1/51 + 1/10302 + 1/10311 + 1/11802658}$ ${\ displaystyle p = 491> 101 = n}$ ${\ displaystyle p}$

Individual evidence

^ RJ Gillings: Mathematics in Time of the Pharaohs. MIT Press, Cambridge (MA) 1972.
^ Abdulrahman A. Abdulaziz: On the Egyptian method of decomposing 2 / n into unit fractions . In: Historia Mathematica. Volume 35, No. 1, February 2008, pp. 1-18.
↑ Carlos Dorce: The Exact Computation of the decompositions of the Recto Table of the Rhind Mathematical Papyrus . In: History Research. Volume 6, No. 2, December 2018, pp. 33-49 ( full text ).
↑ FindInstance [2/101 == 1 / c1 + 1 / c2 + 1 / c3 + 1 / c4 && 0 <c1 <c2 <c3 <c4, {c1, c2, c3, c4}, integers, 3] => FindInstance :: fwsol: Warning: FindInstance found only 1 instance (s), but it was not able to prove 3 instances do not exist. >> {{c1 -> 51, c2 -> 10302, c3 -> 10311, c4 -> 11802658}}

[1] RJ Gillings: Mathematics in Time of the Pharaohs. MIT Press, Cambridge (MA) 1972.

[2] Abdulrahman A. Abdulaziz: On the Egyptian method of decomposing 2 / n into unit fractions . In: Historia Mathematica. Volume 35, No. 1, February 2008, pp. 1-18.

[3] Carlos Dorce: The Exact Computation of the decompositions of the Recto Table of the Rhind Mathematical Papyrus . In: History Research. Volume 6, No. 2, December 2018, pp. 33-49 ( full text ).

[4] FindInstance [2/101 == 1 / c1 + 1 / c2 + 1 / c3 + 1 / c4 && 0 <c1 <c2 <c3 <c4, {c1, c2, c3, c4}, integers, 3] => FindInstance :: fwsol: Warning: FindInstance found only 1 instance (s), but it was not able to prove 3 instances do not exist. >> {{c1 -> 51, c2 -> 10302, c3 -> 10311, c4 -> 11802658}}