Wersja z 2015-09-12

Grzegorz Jagodziński

Ułamki egipskie

1 2 3 4 5 6

Tabela rozkładu ułamków na cztery składniki

ułamek warunek `a` różnica `a` warunki `b` różnica `b` warunek `c` różnica `c` rozkład  
`8/11` `1.38 < a < 5.5` `5` `8/11 - 1/5 = 29/55` `1.90 < b < 5.69`, `b > 5`  
`4` `8/11 - 1/4 = 21/44` `2.10 < b < 6.29`, `b > 4` `6` `21/44 - 1/6 = 41/132` `3.22 < c < 6.44`, `c > 6`
`5` `21/44 - 1/5 = 61/220` `3.61 < c < 7.21`, `c > 5` `7` `61/220 - 1/7 = 207/1540`
`6` `61/220 - 1/6 = 73/660`
`3` `8/11 - 1/3 = 13/33` `2.54 < b < 7.62`, `b > 3` `7` `13/33 - 1/7 = 58/231` `3.98 < c < 7.97`, `c > 7`
`6` `13/33 - 1/6 = 5/22` `4.4 < c < 8.8`, `c > 6` `8` `5/22 - 1/8 = 9/88`
`7` `5/22 - 1/7 = 13/154`
`5` `13/33 - 1/5 = 32/165` `5.16 < c < 10.31` `10` `32/165 - 1/10 = 31/330`
`9` `32/165 - 1/9 = 41/495`
`8` `32/165 - 1/8 = 91/1320`
`7` `32/165 - 1/7 = 59/1155`
`6` `32/165 - 1/6 = 3/110`
`4` `13/33 - 1/4 = 19/132` `6.95 < c < 13.89` `13` `19/132 - 1/13 = 115/1716`
`12` `19/132 - 1/12 = 2/33`
`11` `19/132 - 1/11 = 7/132`
`10` `19/132 - 1/10 = 29/660`
`9` `19/132 - 1/9 = 13/396`
`8` `19/132 - 1/8 = 5/264`
`7` `19/132 - 1/7 = 1/924` `8/11 = 1/3 + 1/4 + 1/7 + 1/924`
`2` `8/11 - 1/2 = 5/22` `4.4 < b < 13.2` `13` `5/22 - 1/13 = 43/286` `6.65 < c < 13.30`, `c > 13`
`12` `5/22 - 1/12 = 19/132` `6.95 < c < 13.89`, `c > 12` `13` `19/132 - 1/13 = 115/1716`
`11` `5/22 - 1/11 = 3/22` `7.33 < c < 14.67`, `c > 11` `14` `3/22 - 1/14 = 5/77`
`13` `3/22 - 1/13 = 17/286`
`12` `3/22 - 1/12 = 7/132`
`10` `5/22 - 1/10 = 7/55` `7.86 < c < 15.71`, `c > 10` `15` `7/55 - 1/15 = 2/33`
`14` `7/55 - 1/14 = 43/770`
`13` `7/55 - 1/13 = 36/715`
`12` `7/55 - 1/12 = 29/660`
`11` `7/55 - 1/11 = 2/55`
`9` `5/22 - 1/9 = 23/198` `8.61 < c < 17.22`, `c > 9` `17` `23/198 - 1/17 = 193/3366`
`16` `23/198 - 1/16 = 85/1584`
`15` `23/198 - 1/15 = 49/990`
`14` `23/198 - 1/14 = 31/693`
`13` `23/198 - 1/13 = 101/2574`
`12` `23/198 - 1/12 = 13/396`
`11` `23/198 - 1/11 = 5/198`
`10` `23/198 - 1/10 = 8/495`
`8` `5/22 - 1/8 = 9/88` `9.78 < c < 19.56` `19` `9/88 - 1/19 = 83/1672`
`18` `9/88 - 1/18 = 37/792`
`17` `9/88 - 1/17 = 65/1496`
`16` `9/88 - 1/16 = 7/176`
`15` `9/88 - 1/15 = 47/1320`
`14` `9/88 - 1/14 = 19/616`
`13` `9/88 - 1/13 = 29/1144`
`12` `9/88 - 1/12 = 5/264`
`11` `9/88 - 1/11 = 1/88` `8/11 = 1/2 + 1/8 + 1/11 + 1/88`
`10` `9/88 - 1/10 = 1/440` `8/11 = 1/2 + 1/8 + 1/10 + 1/440`
`7` `5/22 - 1/7 = 13/154` `11.85 < c < 23.69` `23` `13/154 - 1/23 = 145/3542`
`22` `13/154 - 1/22 = 3/77`
`21` `13/154 - 1/21 = 17/462`
`20` `13/154 - 1/20 = 53/1540`
`19` `13/154 - 1/19 = 93/2926`
`18` `13/154 - 1/18 = 20/693`
`17` `13/154 - 1/17 = 67/2618`
`16` `13/154 - 1/16 = 27/1232`
`15` `13/154 - 1/15 = 41/2310`
`14` `13/154 - 1/14 = 1/77` `8/11 = 1/2 + 1/7 + 1/14 + 1/77`
`13` `13/154 - 1/13 = 15/2002`
`12` `13/154 - 1/12 = 1/924` `8/11 = 1/2 + 1/7 + 1/12 + 1/924`
`6` `5/22 - 1/6 = 2/33` `16.5 < c < 33` `32` `2/33 - 1/32 = 31/1056`
`31` `2/33 - 1/31 = 29/1023`
`30` `2/33 - 1/30 = 3/110`
`29` `2/33 - 1/29 = 25/957`
`28` `2/33 - 1/28 = 23/924`
`27` `2/33 - 1/27 = 7/297`
`26` `2/33 - 1/26 = 19/858`
`25` `2/33 - 1/25 = 17/825`
`24` `2/33 - 1/24 = 5/264`
`23` `2/33 - 1/23 = 13/759`
`22` `2/33 - 1/22 = 1/66` `8/11 = 1/2 + 1/6 + 1/22 + 1/66`
`21` `2/33 - 1/21 = 1/77` `8/11 = 1/2 + 1/6 + 1/21 + 1/77`
`20` `2/33 - 1/20 = 7/660`
`19` `2/33 - 1/19 = 5/627`
`18` `2/33 - 1/18 = 1/198` `8/11 = 1/2 + 1/6 + 1/18 + 1/198`
`17` `2/33 - 1/17 = 1/561` `8/11 = 1/2 + 1/6 + 1/17 + 1/561`
`5` `5/22 - 1/5 = 3/110` `36.67 < c < 73.33` `73` `3/110 - 1/73 = 109/8030`
`72` `3/110 - 1/72 = 53/3960`
`71` `3/110 - 1/71 = 103/7810`
`70` `3/110 - 1/70 = 1/77` `8/11 = 1/2 + 1/5 + 1/70 + 1/77`
`69` `3/110 - 1/69 = 97/7590`
`68` `3/110 - 1/68 = 47/3740`
`67` `3/110 - 1/67 = 91/7370`
`66` `3/110 - 1/66 = 2/165`
`65` `3/110 - 1/65 = 17/1430`
`64` `3/110 - 1/64 = 41/3520`
`63` `3/110 - 1/63 = 79/6930`
`62` `3/110 - 1/62 = 19/1705`
`61` `3/110 - 1/61 = 73/6710`
`60` `3/110 - 1/60 = 7/660`
`59` `3/110 - 1/59 = 67/6490`
`58` `3/110 - 1/58 = 16/1595`
`57` `3/110 - 1/57 = 61/6270`
`56` `3/110 - 1/56 = 29/3080`
`55` `3/110 - 1/55 = 1/110` `8/11 = 1/2 + 1/5 + 1/55 + 1/110`
`54` `3/110 - 1/54 = 13/1485`
`53` `3/110 - 1/53 = 49/5830`
`52` `3/110 - 1/52 = 23/2860`
`51` `3/110 - 1/51 = 43/5610`
`50` `3/110 - 1/50 = 2/275`
`49` `3/110 - 1/49 = 37/5390`
`48` `3/110 - 1/48 = 17/2640`
`47` `3/110 - 1/47 = 31/5170`
`46` `3/110 - 1/46 = 7/1265`
`45` `3/110 - 1/45 = 1/198` `8/11 = 1/2 + 1/5 + 1/45 + 1/198`
`44` `3/110 - 1/44 = 1/220` `8/11 = 1/2 + 1/5 + 1/44 + 1/220`
`43` `3/110 - 1/43 = 19/4730`
`42` `3/110 - 1/42 = 4/1155`
`41` `3/110 - 1/41 = 13/4510`
`40` `3/110 - 1/40 = 1/440` `8/11 = 1/2 + 1/5 + 1/40 + 1/440`
`39` `3/110 - 1/39 = 7/4290`
`38` `3/110 - 1/38 = 1/1045` `8/11 = 1/2 + 1/5 + 1/38 + 1/1045`
`37` `3/110 - 1/37 = 1/4070` `8/11 = 1/2 + 1/5 + 1/37 + 1/4070`
 
`9/11` `1.22 < a < 4.89` `4` `9/11 - 1/4 = 25/44` `1.76 < b < 5.28`, `b > 4` `5` `25/44 - 1/5 = 81/220` `2.72 < c < 5.43`, `c > 5`  
`3` `9/11 - 1/3 = 16/33` `2.06 < b < 6.19`, `b > 3` `6` `16/33 - 1/6 = 7/22` `3.14 < c < 6.29`, `c > 6`
`5` `16/33 - 1/5 = 47/165` `3.51 < c < 7.02`, `c > 5` `7` `47/165 - 1/7 = 164/1155`
`6` `47/165 - 1/6 = 13/110`
`4` `16/33 - 1/4 = 31/132` `4.26 < c < 8.52` `8` `31/132 - 1/8 = 29/264`
`7` `31/132 - 1/7 = 85/924`
`6` `31/132 - 1/6 = 3/44`
`5` `31/132 - 1/5 = 23/660`
`2` `9/11 - 1/2 = 7/22` `3.14 < b < 9.43` `9` `7/22 - 1/9 = 41/198` `4.83 < c < 9.66`, `c > 9`
`8` `7/22 - 1/8 = 17/88` `5.18 < c < 10.35`, `c > 8` `10` `17/88 - 1/10 = 41/440`
`9` `17/88 - 1/9 = 65/792`
`7` `7/22 - 1/7 = 27/154` `5.70 < c < 11.41`, `c > 7` `11` `27/154 - 1/11 = 13/154`
`10` `27/154 - 1/10 = 29/385`
`9` `27/154 - 1/9 = 89/1386`
`8` `27/154 - 1/8 = 31/616`
`6` `7/22 - 1/6 = 5/33` `6.6 < c < 13.2` `13` `5/33 - 1/13 = 32/429`
`12` `5/33 - 1/12 = 3/44`
`11` `5/33 - 1/11 = 2/33`
`10` `5/33 - 1/10 = 17/330`
`9` `5/33 - 1/9 = 4/99`
`8` `5/33 - 1/8 = 7/264`
`7` `5/33 - 1/7 = 2/231`
`5` `7/22 - 1/5 = 13/110` `8.46 < c < 16.92` `16` `13/110 - 1/16 = 49/880`
`15` `13/110 - 1/15 = 17/330`
`14` `13/110 - 1/14 = 18/385`
`13` `13/110 - 1/13 = 59/1430`
`12` `13/110 - 1/12 = 23/660`
`11` `13/110 - 1/11 = 3/110`
`10` `13/110 - 1/10 = 1/55` `9/11 = 1/2 + 1/5 + 1/10 + 1/55`
`9` `13/110 - 1/9 = 7/990`
`4` `7/22 - 1/4 = 3/44` `14.67 < c < 29.33` `29` `3/44 - 1/29 = 43/1276`
`28` `3/44 - 1/28 = 5/154`
`27` `3/44 - 1/27 = 37/1188`
`26` `3/44 - 1/26 = 17/572`
`25` `3/44 - 1/25 = 31/1100`
`24` `3/44 - 1/24 = 7/264`
`23` `3/44 - 1/23 = 25/1012`
`22` `3/44 - 1/22 = 1/44` `9/11 = 1/2 + 1/4 + 1/22 + 1/44`
`21` `3/44 - 1/21 = 19/924`
`20` `3/44 - 1/20 = 1/55` `9/11 = 1/2 + 1/4 + 1/20 + 1/55`
`19` `3/44 - 1/19 = 13/836`
`18` `3/44 - 1/18 = 5/396`
`17` `3/44 - 1/17 = 7/748`
`16` `3/44 - 1/16 = 1/176` `9/11 = 1/2 + 1/4 + 1/16 + 1/176`
`15` `3/44 - 1/15 = 1/660` `9/11 = 1/2 + 1/4 + 1/15 + 1/660`
 
`10/11` `1.1 < a < 4.4` `4` `10/11 - 1/4 = 29/44` `1.52 < b < 4.55`, `b > 4`  
`3` `10/11 - 1/3 = 19/33` `1.74 < b < 5.21`, `b > 3` `5` `19/33 - 1/5 = 62/165` `2.66 < c < 5.32`, `c > 5`
`4` `19/33 - 1/4 = 43/132` `3.07 < c < 6.14`, `c > 4` `6` `43/132 - 1/6 = 7/44`
`5` `43/132 - 1/5 = 83/660`
`2` `10/11 - 1/2 = 9/22` `2.44 < b < 7.33` `7` `9/22 - 1/7 = 41/154` `3.76 < c < 7.51`, `c > 7`
`6` `9/22 - 1/6 = 8/33` `4.13 < c < 8.25`, `c > 6` `8` `8/33 - 1/8 = 31/264`
`7` `8/33 - 1/7 = 23/231`
`5` `9/22 - 1/5 = 23/110` `4.78 < c < 9.57`, `c > 5` `9` `23/110 - 1/9 = 97/990`
`8` `23/110 - 1/8 = 37/440`
`7` `23/110 - 1/7 = 51/770`
`6` `23/110 - 1/6 = 7/165`
`4` `9/22 - 1/4 = 7/44` `6.29 < c < 12.57` `12` `7/44 - 1/12 = 5/66`
`11` `7/44 - 1/11 = 3/44`
`10` `7/44 - 1/10 = 13/220`
`9` `7/44 - 1/9 = 19/396`
`8` `7/44 - 1/8 = 3/88`
`7` `7/44 - 1/7 = 5/308`
`3` `9/22 - 1/3 = 5/66` `13.2 < c < 26.4` `26` `5/66 - 1/26 = 16/429`
`25` `5/66 - 1/25 = 59/1650`
`24` `5/66 - 1/24 = 3/88`
`23` `5/66 - 1/23 = 49/1518`
`22` `5/66 - 1/22 = 1/33` `10/11 = 1/2 + 1/3 + 1/22 + 1/33`
`21` `5/66 - 1/21 = 13/462`
`20` `5/66 - 1/20 = 17/660`
`19` `5/66 - 1/19 = 29/1254`
`18` `5/66 - 1/18 = 2/99`
`17` `5/66 - 1/17 = 19/1122`
`16` `5/66 - 1/16 = 7/528`
`15` `5/66 - 1/15 = 1/110` `10/11 = 1/2 + 1/3 + 1/15 + 1/110`
`14` `5/66 - 1/14 = 1/231` `10/11 = 1/2 + 1/3 + 1/14 + 1/231`