kutaka

Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ax + by = c where x and y are unknown quantities and a, b, and c are known quantities with integer values. The algorithm was originally invented by the Indian astronomer-mathematician Āryabhaṭa (476–550 CE) and is described very briefly in his Āryabhaṭīya. Āryabhaṭa did not give the algorithm the name Kuṭṭaka, and his description of the method was mostly obscure and incomprehensible. It was Bhāskara I (c. 600 – c. 680) who gave a detailed description of the algorithm with several examples from astronomy in his Āryabhatiyabhāṣya, who gave the algorithm the name Kuṭṭaka. In Sanskrit, the word Kuṭṭaka means pulverization (reducing to powder), and it indicates the nature of the algorithm. The algorithm in essence is a process where the coefficients in a given linear Diophantine equation are broken up into smaller numbers to get a linear Diophantine equation with smaller coefficients. In general, it is easy to find integer solutions of linear Diophantine equations with small coefficients. From a solution to the reduced equation, a solution to the original equation can be determined. Many Indian mathematicians after Aryabhaṭa have discussed the Kuṭṭaka method with variations and refinements. The Kuṭṭaka method was considered to be so important that the entire subject of algebra used to be called Kuṭṭaka-ganita or simply Kuṭṭaka. Sometimes the subject of solving linear Diophantine equations is also called Kuṭṭaka.
In literature, there are several other names for the Kuṭṭaka algorithm like Kuṭṭa, Kuṭṭakāra and Kuṭṭikāra. There is also a treatise devoted exclusively to a discussion of Kuṭṭaka. Such specialized treatises are very rare in the mathematical literature of ancient India. The treatise written in Sanskrit is titled Kuṭṭākāra Śirōmaṇi and is authored by one Devaraja.The Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day extended Euclidean algorithm. The latter algorithm is a procedure for finding integers x and y satisfying the condition ax + by = gcd(a, b).

View More On Wikipedia.org
Recent contents
  1. F

    JamiiForums Tanzania Kila mtu kutaka kuwa Mwanasiasa ni dalili ya Taifa masikini lililokosa mwelekeo

    Kwa muda mrefu nimekuwa nikijua kuwa dalili mojawapo ya Taifa masikini ni kuwa na wakulima wengi! Tanzania ina wakulima kati ya 65% hadi 80% katika population ya watu milioni 60, hivyo hili ni Taifa masikini sana! Marekani yenye watu zaidi ya milioni 300 ina wakulima wasiozidi asilimia 10%...
  2. M

    JamiiForums Tanzania Watanzania tusiopenda Unafiki na Ng'ombe Kunenepeshwa Siku ya Mnada na kutaka Congo DR na Madagascar watufunge tujuane tafadhali

    Wala nisiwafiche baada ya kuona Watu wa Yanga SC ( tena kutokea GSM ) ambao KEROZENE siwapendi na nawachukia ndiyo wamepewa Kipaumbele kwa Maandalizi ya Taifa Stars nimeuza Siri zote za Kambi ya Taifa Stars na Alhamisi Tanzania ikishinda ni Sare ila Kufungwa ni kama Israeli na Roho ya Binadamu...
    • MINOCYCLINE
    • Thread
    • congo kutaka madagascar mnada ng'ombe siku tafadhali unafiki watanzania
    • Replies: 15
    • Forum: Jamii Sports
  3. Cvez

    JamiiForums Tanzania Maprofesa kutaka kuongezewa muda wa Kustaafu ni ubinafsi wa hali ya juu

    Ni kweli tuna unapungufu wa wanataaluma katika vyuo vyetu ila haijatokea kwa bahati mbaya. Katika vyuo vyetu hivi kama huna Surname inayofanania ni na Profesa fulani kupata nafasi ya ukufunzi hiyo ni ndoto. Katika sehemu ambazo kwa kiasi kikubwa zimejaa undugu na kujuana kwa kiasi kikubwa ni...
  4. L

    JamiiForums Tanzania China na Afrika zikiendelea kuuenzi uhusiano wao ustawi, kuna wale wanaozusha vijineno vya chini chini vya kutaka kuusambaratisha

    Na Pili Mwinyi Ingawa uhusiano wa kidiplomasia kati ya China na Afrika ulianzishwa katikati ya miaka ya 50, lakini hivi sasa uhusiano huu unaendelea kukua na kustawi na umekuwa ukiimarishwa siku hadi siku, ambapo pande zote mbili zinaungana mkono kwenye masuala mbalimbali. Hata hivyo kuna wale...
  5. YEHODAYA

    JamiiForums Tanzania Suala la kuajiri kwa kutaka mtu awe kapitia JKT liangaliwe upya, JKT huwa hawachukui wote wanaomaliza kidato cha sita mafunzoni

    Ni kawaida Kila mwaka JKT kuchukua wanafunzi wa kidato Cha sita na kuwapangia kambi za mafunzo ya JKT wanakotakiwa kuripoti.Lakini huwa hawachukui wote waliomaliza form six huchukua wachache na wengine kuachwa Sasa linapokuja suala la ajira mtu hutakiwa awe na cheti Cha JKT Sasa huyo ambaye...
  6. Analogia Malenga

    JamiiForums Tanzania Mwanza: Wamachinga waandamana kutaka kupewa vizimba katika maeneo waliyopangiwa

    Ni patashika. Ndivyo unavyoweza kuelezea mvutano kati ya wafanyabiashara wadogo jijini Mwanza na mamlaka ya Jiji hilo baada ya wafanyabiashara hao kuandamana leo Jumamosi Oktoba 23,2021 na kufunga barabara ya Nyerere eneo ya Voil kushinikiza kupewa vizimba kwenye maeneo rasmi. Kundi la...
  7. mirindimo

    JamiiForums Tanzania Mambo 30 usiyoyajua kuhusu utapeli wa Q-Net (Network Marketing)

    Habari wadau, niliwahi kuja na uzi hapa kuhusu D09 CLUB Miezi michache kabla haijapotelea kusikojulikana na nilishambuliwa sana na waliliwa pesa zao na bila kujua hatma yao wanarudishiwa vipi na nani. Leo naomba nije na mambo 30 usiyoyajua kuhusu Qnet. Qnet ni network marketing ambayo imevuta...
  8. kindikinyer leborosier

    JamiiForums Tanzania Tupeane ujuzi: Kabla ya kuoa, dada zetu na mama zetu wanayapokeaje mawazo ya sisi kutaka kuoa?

    Habari wanajamvi, poleni na majukumu ya kila siku! . . niende moja kwa moja kwenye mada, kwa mara ya kwanza kusema nyumbani kuwa unataka kuoa, dada zako na mama walichukuliaje?. . . binafsi mimi ni kijana wa miaka 30 kwa sasa, nina mchumba tayari, lakini imekuwa kila nikisema nyumbani hata kwa...
  9. S

    JamiiForums Tanzania Hizi picha miaka 60 baada ya uhuru, ni kielelezo tulikosea kutaka kujitawala na tulitakiwa tuendelee kutawaliwa

    Ukiacha swala zima la utawala bora na mambo mengineyo yaliyotushinda mpaka sasa, hata hili la vyumba vya madarasa na matundu ya choo,nalo bado ni tatizo miaka 60 tangu tuanze kujitawala. Cha ajabu, 2025 CCM watataka tena wachaguliwe ili waendelee kuongoza hii nchi na kuna watu watawapigia...
  10. kmbwembwe

    JamiiForums Tanzania Tunaposikia ya Makamba na Zitto kutaka kubinafsisha TANESCO, tukumbuke yaliyofanyika TTCL

    Kuna mashirika ya Serikali kutokana na wajibu wake ni kama idara za Serikali. Yanatakiwa yagharamikiwe na hazina kuu. Yanafanywa mashirika ili kuweza kudhibiti matumizi na kwamba iwepo tija. Ukitaka kugeuza TANESCO liwe la kibiashara moja kwa moja kwanza utapata muwekezaji gani? Lazima awe wa...
  11. Idugunde

    JamiiForums Tanzania Sakata la Mbowe kuwa na tuhuma za ugaidi isiwe sababu ya kutaka Watanzania tuamini anaonewa. Tuache mahakama iamue.

    Kila mwanaChadema anataka kuwaaminisha watanzania kuwa Mbowe amebambikizwa shitaka la ugaidi. Mbowe anaonewa maana sasa amewekwa kwenye sero ya wafungwa wa kunyongwa. Sawa, mnaweza kuwa sawa lakini suala lipo mahakamani. Ibara ya 13 ya JMT ipo wazi kabisa kuwa hakuna mtu atakuwa na hatia mpaka...
    • Idugunde
    • Thread
    • kutaka mahakama mbowe sababu sakata tuache tuhuma ugaidi watanzania
    • Replies: 27
    • Forum: Jukwaa la Siasa
  12. DR HAYA LAND

    JamiiForums Tanzania Ni vizuri watu mkawa makini Mtu kama Mh. Mbowe yuko na Mtaji wa watu hivyo kutaka kumpoteza nikujilisha upepo tu.

    Unfortunately hii Serikali inajilisha upepo , kupoteza Fedha na hela za walipa kodi kwa ajili ya kulifuta jina linaoitwa Mbowe ni kujidanganya. Hii ni sawa na mtu kuchota maji mtoni na kuyapeleka baharani. Mbowe yuko na back up ya watu almost Million 30 Tz na nje. Mimi naona hii ligi...
  13. Kipenzi Changu

    JamiiForums Tanzania Hongera Yanga kwa kutaka kurejesha ubingwa wenu wa CAFCL

    Huku ni kudhalilishana tu. Watu wa kimataifa mnaposikia hiyo slogan msije mkachukulie watz wote mabogus. Hapana,ni kikundi kidogo tu kimeamua kinaitwa Utopolo. Waambieni watu Return hii ni kwa mbeleko ya Simba SC
  14. S

    JamiiForums Tanzania Rais Samia atoa pole kufuatia mauaji Daraja la Salender, ataka uchunguzi ufanyike

    Salamu zake ni hizi: Natoa pole kwa Jeshi la Polisi na familia za Askari 3, na Askari 1 wa kampuni ya ulinzi ya SGA waliopoteza maisha baada ya mtu aliyekuwa na silaha kuwashambulia katika eneo la Salenda, Dar es Salaam. Mtu huyo amedhibitiwa na hali ni shwari. Nawaagiza Polisi kuchunguza kwa...
    • Salary Slip
    • Thread
    • jeshi la polisi kutaka rais samia rambirambi salamu za pole uchunguzi
    • Replies: 71
    • Forum: Jukwaa la Siasa
  15. M

    JamiiForums Tanzania Je, wale wenye dhamana za Kisiasa na Kiutawala mmeshajiuliza ni kwanini baadhi yenu mkipata ajali na kunusurika watu hufurahi na hata kutaka mfe tu?

    Kwa lugha nyepesi tu au kwa maana nyingine hapa nasema kuwa tujitahidi mno kabla hatujateuliwa nafasi yoyote au hata tukiteuliwa tu tuache Kuwatendea mabaya Watu kwani Mungu aliyekuumba Wewe ndiyo huyo huyo kawaumba na Wao. Kuna mahala fulani hivi nimemuona Israeli kama vile anataka Kuondoka na...
  16. Idugunde

    JamiiForums Tanzania CHADEMA waombe radhi Umma wa Watanzania kwa kutaka kuleta uvunjifu wa Amani japokuwa wamedhibitiwa

    Mpaka sasa hivi wamedhibitiwa kwa maghasia waliokuwa wanaratibu kuyafanya kwa kisingizio cha kutaka kudai katiba mpya. Madhari hiki ni Chama cha Umma na kwa kuwa kipo chini ya mwavuri wa msajiri wa vyama vya siasa. Basi wanapaswa kuomba radhi ili umma wa watanzania wawasamehe. My take: Kuwa na...
  17. T

    JamiiForums Tanzania Inaonekana RC Makalla anaiongoza Dar, aidha asiyoijua kabisa au kwa kutaka sifa tu

    Ndugu wanabodi kama mtakumbuka vizuri, tukiwa mwanzoni kabisa mwa kukabiliana na changamoto ya COVID-19 mwaka uliopita, ni Serikali hii hii iliamuru level seat kwa daladala zote zinazofanya kazi hapa mkoani Dar. Mara tu baada ya amri hiyo, hali ya usafiri wa umma ilikuwa tete, kwani...
  18. S

    JamiiForums Tanzania Mtego: Wanafanya kila mbinu kutaka wafuasi wa CHADEMA waandamane ili wapate sababu ya kuifuta CHADEMA

    CCM sio tena chama cha siasa, bali ni kakikundi cha watu walioamua kutumia dola kulinda madaraka waliyonayo(kubaki madarakani) Kwa sasa wamegundua kutumia mabavu kupambana na upinzani hasa CHADEMA hakusaidii hivyo wamekuja na mkakati wa kutaka kuifuta CHADEMA kama alivyosema Katibu Mkuu wa...
  19. DR HAYA LAND

    JamiiForums Tanzania Kuifuta CHADEMA au CCM ni sawa na kutaka Yanga ishuke daraja ibaki Simba

    Investment kubwa hapa dunian nikuwekeza katika watu. Chadema haitoweza kufutika hapa Tanzanian kama ilivyo CCM hivi vyama, vitamake headlines mpaka mwisho. Just imagine hawako bungeni lakini bado ni threat kwa serikali ya CCM. Pendekezo amani ya nchi inabidi kupewa kipaumbele kwa kutoa Haki...
  20. S

    JamiiForums Tanzania Freeman Mbowe, nchi kuongozwa na Mwanamke siyo fursa ya kutaka mambo kwa pupa

    Kuna wakati kila jambo linahitaji kufikiriwa kwa undani sana, kila mtu katika taifa ana haki yake lakini katika kudai haki yako kuna taratibu nyingi za kufuata pamoja na kufanya uzingativu hivyo ukikosea katika utaratibu huo basi haki yako inageuka kuwa kaa la moto hata kama ni jambo la faida...

Our Community

Coming Soon

Regional Communities

Coming Soon
Back
Top Bottom
Menu
Forums
New posts
Log in
Register