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. M

    Shura ya Maimamu wa Tanzania yatoa waraka mzito-Yalaani matendo ya utekaji na mauaji nchini na kutaka haki katika chaguzi nchini

    HAYA NI BAADHI YA MAMBO YALIYOMO KATIKA WARAKA WA SHURA YA MAIMAMU , WARAKA MZIMA UPO KATIKA ATTACHMENT SHURA YA MAIMAMU TANZANIA S.L.B.2055 DAR ES SALAAM. 0748410746 WARAKA WA IDD ADH-HAA DHULHIJJA 10, 1446 = JUNI 07, 2025 PITIO LA HALI YA MAISHA TANZANIA 2025 Uchaguzi Mkuu Oktoba 2025...
    • Missile of the Nation
    • Thread
    • chaguzi haki katika kutaka matendo mauaji mauaji nchini nchini shura ya maimamu tanzania utekaji utekaji na mauaji waraka
    • Replies: 37
    • Forum: Jukwaa la Siasa

  2. Tabia za baadhi ya wanawake kutaka wapewe pesa na zawadi zinawafanya wanaume weengi kuamini kuwa tendo la ndoa halina umuhimu kwa mwanamke

    Inaweza ikakushangaza lakini huu ndio ukweli wenyewe. Katika jamii zetu za kiafrika wanawake walio wengi wanakuwa hawapo tayari kushiriki tendo pasipo ahadi ya kupewa pesa au zawadi fulani. Yaani ili mwanamke akupe tendo basi ni lazma utoe kitu flani. Hali hii inafanya wanaume wengi kuamini...

  3. Baraza la Usalama la Umoja wa Mataifa leo litapigia kura azimio la kutaka kusitishwa mara moja kwa mapigano huko Gaza

    Baraza la Usalama la Umoja wa Mataifa leo litapigia kura azimio la kutakao kusitishwa mara moja kwa mapigano huko Gaza. Azimio hilo haliwekei masharti ya kusitisha mapigano kwa kuachiliwa kwa mateka waliosalia. Kwa maneno mengine, inawaacha Hamas madarakani, wakiwa na silaha, na kuwashikilia...
    • Echolima1
    • Thread
    • azimio baraza baraza la usalama gaza kura kusitishwa kutaka mapigano mara mataifa moja umoja umoja wa mataifa usalama
    • Replies: 5
    • Forum: International Forum
  4. U

    Fatma Karume amlipua Gwajima kwa kutaka Misikiti kugeuzwa Sunday Schools

    Katika chapisho lenye maneno makali kwenye mtandao wa X (zamani Twitter), mwanasheria na mwanaharakati mashuhuri Fatma Karume amemshambulia vikali Mbunge wa Kawe, Askofu Josephat Gwajima, kwa nia ya kutaka “misikiti igeuzwe kuwa Sunday Schools.” Kauli hiyo imeibua mjadala mzito kuhusu uhuru wa...

  5. PreGE2025 Tarimba: Yeyote yule akionesha ishara za kutaka kuipasua CCM, tutampasua yeye kwanza

    Mbunge wa Jimbo la Kinondoni na Mjumbe wa Mkutano Mkuu wa CCM, Abbas Tarimba, amesema kuwa Chama Cha Mapinduzi (CCM) ni taasisi imara isiyoweza kuyumbishwa na mtu yeyote mwenye nia ovu ya kukipasua. Akizungumza katika viwanja vya Jakaya Kikwete Convention Centre jijini Dodoma, Tarimba alisema...
  6. M

    Waraka wa Mabadiliko Je Zitto alikuwa sahihi kutaka kumng'oa Mbowe?

    Sote tunaona yanayoendelea ndani ya CHADEMA ya leo. Uchaguzi ndani ya chama umezaa kizaazaa baada ya madalali wa kisiasa nchini kupigwa chini. Takriban miaka 12 iliyopita, wakati huo Kijana Zitto Kabwe, Kitila Mkumbo na Samson Mwigamba walipanga mkakati wa kumng'oa Freeman Mbowe, hoja yao kuu...

  7. Is it fair kumhukumu mdada kwa kutaka kuwa na bwana mwenye pesa zaidi?

  8. Wenye kutaka tshirt za hatuchezi mbele mpambane na hali zenu tuwasiliane nbox

    Kwa wana Yanga tu Kuna tshirt za hatuchezi zinanza kutoka jmosi Na mbele mpambane na hali zenu Tuwasiliane nbox

  9. Ni wazi kujiondoa kwa G55 kuna ajenda ya siri ya kutaka kuyumbusha chama lakini hii nayo inampigia promo Lissu duniani kote

    Kila mmoja anajua na hata ualaya wanajua Lissu amehamasisha uwepo wa uchaguzi huru na wa haki nchini, sasa anae waelewa hawa G55 aje anieleweshe wanapinga nini ? kwenye mabadiliko hayo na progamu hiyo ya chama. Ukiangalia vizuri hawa G55 wana ajenda ya siri nyuma ya pazia au wametumwa na mtu...
    • Genius Man
    • Thread
    • ajenda chama duniani g55 hii kutaka lissu nafikiri nayo promo siri wazi
    • Replies: 24
    • Forum: Jukwaa la Siasa

  10. Mwanamke kutaka mwanaume a'provide kwao ni lazima ila kumheshimu na kumtii mwanaume ni option

    Ukitazama kwenye mahusiano ya watu wengi utagundua kuwa wanawake hudhania kumtii mwanaume,kusikiliza maagizo yake na kuyafanyia utekelezaji bila kuhoji maswali yasiyo ya lazima,kuwa msikilizaji mzuri na sio mzinguaji au mpinzani, kuwa mshirika na sio hasimu, hivi vyote kwao hudhania ni option...
    • Zemanda
    • Thread
    • heshima kwenye mahusiano kutaka kutii mwanaume kwao lazima mwanaume option provide thamani ya mwanamke
    • Replies: 7
    • Forum: Mahusiano, mapenzi, urafiki

  11. Sababu mojawapo ya kutaka Stellenbosch wafungwe na Simba ni hizi dharau za wasouth

    Asubuhi asubuhi nadondosha uzi. Ebwana wasouth wana dharau sana kwa waafrika wenzao. Yaani hawa jamaa tumewapigania na tuliwapa hadi hifadhi lakini leo wanatuona waafrika wenzao kama nyani na ngedere. Wanatuona kama binadamu ambao hawajastaarabika. Kuna video nimeiona jana usiku wakiiongelea...

  12. Nakumbuka siku Mbowe alipotaka kulitumia kanisa kutaka kuvunja katiba na akashindwa.Sijui itakuwaje kwa Lisu baada kanisa kurudi tena.

    Chadema chini ya Freeman Mbowe walibadili ajenda ghafla baada ya kufa kwa kada wao na kufanya vuguvugu la kutaka kumpindua raisi aliye madarakani. Siku ilipofika wakamuingiza chaka mpaka baba askofu ambaye alitumia redio za kanisa kuwashawishi wafuasi wa Chadema wajiunge kwenye maandamano.Kwa...
  13. M

    Kutaka kila mtu akuongelee vizuri ni kutafuta msongo wa mawazo kuwa mwema ila usijali watakavyokuongelea

    KUTAKA KILA MTU AKUONGELEE VIZURI NI KUTAFUTA MSONGO WA MAWAZO KUWA MWEMA ILA USIJALI WATAVYOKUONGELEA Zama zinaenda kasi na vifo vitokanavyo na matokeo ya msongo wa mawazo vikiongezeka ikiwemo kujiua au shinikizo la juu la damu hata magonjwa ya moyo. Msongo wa mawazo hautoki mbinguni bali ni...

  14. Mzee Dalali nakuheshimu sana na acha kabisa kutaka Kuwadanganya wana Simba SC kuwa sijui Yanga SC wanatuhujumu ili tufungwe Keshokutwa na Al Masry

    “Kuna watu hawataki tuendelee hivyo wanawatumia baadhi ya watu wetu wa ndani. Wanasimba wote njoeni uwanjani, na jamaa pia njoeni muone, hata wakitaka wavae misuli njoeni kushangilia timu yetu. Lakini nawambia tarehe 9 mwarabu atatafuta sehemu ya kupitia.”- Mwenyekiti wa zamani wa Simba, Hassan...
    • GENTAMYCINE
    • Thread
    • dalali kutaka mzee sana simba simba sc yanga yanga sc
    • Replies: 25
    • Forum: Jamii Sports

  15. Haya wale ambao mnamtetea Ali Kamwe na Utoto, Upuuzi na kutaka Kwake Sifa zinazoenda Kumtokea puani sasa mjibuni huyu Dada kama mna Hoja za maana

    "Naomba mamlaka husika za mpira wa miguu kwa maana ya TFF na Bodi ya ligi kuchukulia hatua jambo hili, Bodi ya ligi hawajawahi kusema wasemaji tutukane viongozi na nampa masaa 24 Ali Kamwe amuombe msamaha mkuu watu wa mkoa Paul Chacha."- Christiana Mwagala ( @mwagala.christina) Afisa Habari wa...
    • GENTAMYCINE
    • Thread
    • ali kamwe dada haya hoja kamwe kutaka maana sifa utoto
    • Replies: 20
    • Forum: Jamii Sports

  16. Haya wale ambao mnamtetea Ali Kamwe na Utoto, Upuuzi na kutaka Kwake Sifa zinazoenda Kumtokea puani sasa mjibuni huyu Dada kama mna Hoja za maana

    "Naomba mamlaka husika za mpira wa miguu kwa maana ya TFF na Bodi ya ligi kuchukulia hatua jambo hili, Bodi ya ligi hawajawahi kusema wasemaji tutukane viongozi na nampa masaa 24 Ali Kamwe amuombe msamaha mkuu watu wa mkoa Paul Chacha."- Christiana Mwagala ( @mwagala.christina) Afisa Habari wa...
    • GENTAMYCINE
    • Thread
    • ali kamwe dada haya hoja kamwe kutaka maana sifa utoto
    • Replies: 7
    • Forum: Jamii Sports

  17. Nimemkumbuka Mzee Mbowe na Asali alolambishwa kutaka kumfuta Mh LISSU kwenye Siasa za Upinzani.

    Duuh vita ikawa Kali sana, Mzee Mbowe akawa anataka Uenyekiti, hapohapo anataka Agombee Urais 🤣. Kumbe Lengo akiwa Mwenyekiti autumie kuwabana akina Lissu , Heche . Agombee Urais yeye, ili Samia apate Mpinzani lojolojo . Hatimaye Mzee Mbowe, akaangukia PUAA !!.

  18. Maelfu ya watu waandamana kaskazini ya Gaza kupinga vita, wakiimba hatutaki kufa na damu za watoto wetu sio nyepesi.Acha vita.

    Kulingana na shirika la habari la kipalestina la Wafa,maelfu ya watu yaliingia kwenye vichohcoro vya vifusi vya nyumba zao zilizovunjwa wakiimba kwa sauti huku wamebeba mabango wakisema hawataki tena kufa na hakuna kuhama. Kimsingi maandamano hayo yalikuwa ni kupinga vita visiendelee na wala sio...
    • Webabu
    • Thread
    • damu gaza israel kaskazini kufa kupinga kutaka maelfu vita waandamana watoto watoto wetu
    • Replies: 28
    • Forum: International Forum

  19. Tetesi: Barcelona wamepanga kuweka dau kubwa la kutaka kumnunua tena Messi

    Barcelona wamepanga kuweka dau kubwa la kutaka kumnunua tena Lionel Messi kabla ya msimu wa 2026/27, kwa mujibu wa ripoti kutoka nchini Argentina. Messi alihudumu Barcelona kwa zaidi ya miongo miwili huko Catalonia kuanzia mwaka 2000 mpaka msimu wa joto wa 2021, akijiunga na Paris Saint-Germain...
    • Wakusoma 12
    • Thread
    • argentina barcelona dau kabla kubwa kutaka kutoka kuweka lionel messi msimu nchini ripoti tena
    • Replies: 5
    • Forum: Jamii Sports

  20. Tetesi: Inaelezwa Ali Kamwe kafungiwa miaka 2, Ahmed Ally anusurika na rungu la TFF

    Wakuu Kama kweli adhabu ndio hizi una mtazamo gani? Kuna kitu kitapungua kwenye Soka la Bongo? Ikumbukwe, Mameneja hao wa Habari na Mawasiliano wa vilabu vya Simba Sc na Yanga Sc, Ahmed Ally na Ally Kamwe wote waliitwa kwenye Kamati ya Maadili ya Shirikisho la Mpira wa Miguu nchini (TFF)...
    • Waufukweni
    • Thread
    • ahmed ally ali kamwe ally kamwe derby march 8 derby ya kariakoo habari jumamosi kamwe kamwe afungiwa kufungiwa kutaka simba na yanga soka la bongo ujinga
    • Replies: 97
    • Forum: Jamii Sports
Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…