Perbezaan antara semakan "Aryabhata"

16 bait ditambah ,  5 bulan lalu
=== Persamaan tidak tetap ===
 
AMasalah problemyang ofsangat greatmenarik interest tobagi [[Indianahli matematik mathematiciansIndia]] sincesejak ancientzaman timesdahulu hasadalah beenuntuk tomencari findpenyelesaian integer solutionsuntuk topersamaan equationsyang thatmempunyai have the formbentuk ax + b = cy, atopik topicyang thatkemudian hasdikenali come to be known assebagai [[persamaan diophantine equations]]. ThisIni isadalah ancontoh exampledari fromkomen [[Bhaskara]]'s commentary onmengenai Aryabhatiya:
: Cari nombor yang memberikan 5 selebihnya apabila dibahagi dengan 8, 4 selebihnya apabila dibahagi dengan 9, dan 1 selebihnya apabila dibahagi dengan 7
: Find the number which gives 5 as the remainder when divided by 8, 4 as the remainder when divided by 9, and 1 as the remainder when divided by 7
That isMaksudnya, findcari N = 8x+5 = 9y+4 = 7z+1. ItTernyata turnsnilai outterkecil that the smallest value foruntuk N isadalah 85. InSecara generalumum, persamaan diophantine equations, such asseperti thisini, cansangat be notoriously difficultsukar. TheyMereka weredibahas discussedsecara extensivelyluas indalam ancientteks VedicVeda textkuno [[Sulba Sutras]], whoseyang morebahagiannya ancientlebih partskuno mightmungkin dateberasal todari 800 BCESM. Kaedah Aryabhata's methoduntuk ofmenyelesaikan solvingmasalah suchtersebut problemsdisebut is called thekaedah ''{{IAST|kuṭṭaka}}'' (कुट्टक) method. ''Kuttaka'' meansbermaksud "pulverizingmenghancurkan" oratau "breakingmemecahkan intokepingan small pieceskecil", anddan thekaedah methodini involvesmelibatkan aalgoritma recursiverekursif algorithmuntuk formenulis writingfaktor theasal originaldalam factorsjumlah inyang smallerlebih numberskecil. TodayKini thisalgoritma algorithmini, elaboratedyang bydihuraikan oleh Bhaskara inpada tahun 621 CEM, isadalah thekaedah standardpiawai methoduntuk formenyelesaikan solving first-orderpersamaan diophantine equationsperingkat andpertama isdan oftensering referreddisebut to as thesebagai [[algoritma Aryabhata algorithm]].<ref>
Amartya K Dutta, [http://www.ias.ac.in/resonance/Oct2002/pdf/Oct2002p6-22.pdf "Diophantine equations: The Kuttaka"], ''Resonance'', October 2002. Also see earlier overview: [http://www.ias.ac.in/resonance/April2002/pdf/April2002p4-19.pdf ''Mathematics in Ancient India''].</ref> ThePersamaan diophantine equationsmenarik are of interest inminat [[cryptology]], and thedan [[RSA Conference]], 2006, focusedtertumpu onpada thekaedah ''kuttaka'' method and earlierdan workkarya insebelumnya thedi [[Sulvasutras]].
 
=== Algebra ===
Pengguna awanama