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. JamiiForums Tanzania Mbunge Musukuma uwe unatumia akili, sio kutaka sifa zisizo na mashiko. Wewe umesoma na una PhD

    Mtu amesoma na ana Phd lakini anaingilia suala ambalo lina mkataba kisheria. Kama muwekezaji ameingia kima kosa basi halmashauri au waliofunga nae mkataba wauvunje kama kweli ni voidable contract. Sasa habari ya kutaka upewwa maelezo kibabe mbele ya kamera ya nini? Wewe sio sehemu ya mkataba...

  2. JamiiForums Tanzania Jaribo la TRUMP kutaka kumkamata KHAMENI, Ulimwengu una cha kujifunza kuhusu RUSSIA

    Tayari Manowari za Kivita zenye ndege za kutosha, zimeaanza kuelekea Middle East Nimesoma source moja, hadi ndege zinazojaza mafuta ndege nyingine angani zimeshasogezwa hapo Middleeast Kifupi RUSSIA kawasaliti allied wake wote VENEZUELA, CUBA na IRAN. Sijui Viongozi wa Afrika wanakubaligi...

  3. JamiiForums Tanzania Tatizo la magonjwa ya akili duniani limekuwa kubwa sana. Dalili moja ya ugonjwa wa akili ni kutaka kusikia shari kila muda.

    Mtu mwenye matatizo ya akili akisikia mahali kuna ajari anapata furaha moyoni. Akisikia wamekufa wachache au hakuna maiti kwenye ajari hiyo basi moyo wake hupoteza furaha. Akisikia Iran kuna vita anapata raha sana. Mostly ya watu ambao wanajifanya kuchukizwa na mauaji ya October 29 -31 moyoni...
  4. M

    JamiiForums Tanzania Wafanyabiashara soko la Mabibo: RC Chalamila alikuja sokoni akaishia kututukana. Tukapewa kesi ya kutaka kuchoma gari la serikali

    Wafanyabiashara wa soko la mabibo wafunguka kutukanwa na Mkuu wa mkoa wa Dar es Salaam mbele ya Waziri Mkuu wa Jamhuri ya muungano wa Tanzania Dkt Mwigulu Nchemba.

  5. JamiiForums Tanzania Lengo lao la kutaka CCTV camera ziwe na usajili ni nini?

    Turudi nyuma tukio la lissu kupigwa risasi eneo wanapoishi wabunge.CCTv zote ziliondolewa na kulikuwa hakuna usajili. Nilichogundua sehemu zita kazokuwa na CCTv wakifanya utekaji wao wataweza kuzibiti taarifa na kukanusha kama hakuna tukio. Na huu usajili utaweza kujua jirani ,location na wapi...

  6. JamiiForums Tanzania Mtu hawezi kuua watu vile kama hana ushirika na jeshi, nchi zenye jeshi lenye msimamo asingefanya yale, jeshi ni la kulaumiwa sana

    Mtu hawezi kuua watu vile kama hana ushirika na jeshi, nchi zenye jeshi lenye msimamo kama wa Gen Z asingefanya yale, jeshi ni la kulaumiwa sana
    • Genius Man
    • Thread
    • binafsi gen z hana hawezi jaribio jeshi kulaumiwa kutaka kutumika msimamo mtu mtu binafsi nchi nchi yetu sana ushirika
    • Replies: 31
    • Forum: Jukwaa la Siasa

  7. JamiiForums Tanzania Tuhuma dhidi ya Tume ya Jaji Chande kutaka kumsaidia Hangaya dhidi ya mauaji ya Mo29

    KUTOKA kwa Hilda Newton Baada ya kuona watu wamegoma kwenda kutoa maoni sasa wameanza kufuata watu inbox. Mnataka watu waje kutoa maoni ili mumsaidie Idd Amin Mama kujua mashaidi ambao anajua wataenda kumkaanga ICC ili awamalize kabla kesi haijaanza. Kwanza si Idd Amin Mama keshawambia...
    • Msanii
    • Thread
    • chande dhidi jaji jaji chande kumsaidia kutaka mauaji mo29 tuhuma tume tume ya jaji chande
    • Replies: 0
    • Forum: Jukwaa la Siasa
  8. M

    JamiiForums Tanzania Nani anawatumia Gen z kutaka kuangusha dola? Au ndio Mapinduzi kama ya Cuba?

    Rais Samia alisema akiwa anawahutubia wazee wa Dar. Kuwa tar 29 oktoba kuna watu walipanga kuangusha dola. Ndio maana nguvu kubwa ikatumika kuua watu wasio na hatia. Nani anataka kuchukua kiti cha urais kupitia Gen z? Je , haya yanayonukia sio mapinduzi kama ya Cuba ili kuondo mafisadi...

  9. JamiiForums Tanzania PostGE2025 Mashekhe waliotoa kauli za kutaka kuchinja waandamanaji wamechukuliwa hatua gani ?

    Mashekhe ubwabwa waliotoa kauli za kutaka kuchinja waandamanaji wamechukuliwa hatua gani ? Hakuna uwajibikaji tukutane tarehe #D9 tutawawajibisha wenyewe

  10. JamiiForums Tanzania Kwanini Mwanaccm Samia Suluhu Hassan kabadilli gia angani na kutaka kamati mpya ya Uchunguzi?

    Kwanini Mwanaccm Samia Suluhu Hassan kabadilli gia angani na kutaka kamati mpya ya Uchunguzi? Kwani ile ya kwanza nani aliiunda? Asiongeze watu, bali aivunje kabisa.
    • figganigga
    • Thread
    • angani kamati kutaka mpya samia samia suluhu samia suluhu hassan suluhu uchunguzi
    • Replies: 7
    • Forum: Jukwaa la Siasa

  11. JamiiForums Tanzania Watanzania walioko ughaibuni waandamana kutaka haki Tanzania

  12. R

    JamiiForums Tanzania PostGE2025 Siku 100 za Rais Samia zimeanza na Mauaji, kesi za Uhaini kwa Vijana na kutaka maridhiano batili

    Wakuu, Tujikumbushe kidogo wakati Rais Samia akiwa Mgombea Urais wa Chama cha Mapinduzi (CCM) katika ufunguzi wa Kampeni kitaifa uliofanyika Jijini Dar es Salaam katika viwanja vya Kawe, alizungumzia Sera zake na mambo atakayotimiza kwa wananchi ndani ya siku 100. Soma GE2025 - Ahadi za...
    • Richer
    • Thread
    • batili kesi kesi za uhaini kutaka maridhiano mauaji rais rais samia samia siku siku 100 uhaini vijana
    • Replies: 5
    • Forum: Jukwaa la Siasa

  13. JamiiForums Tanzania Tukiwa wakweli, kuna kosa la uhaini wakati serikali inayodhaniwa kutaka kupinduliwa ilikuwa bado kuchaguliwa wala kuundwa?

    Kosa la uhaini uhusisha nia, kujaribu, hata kutenda kitendo cha kutaka kuiangusha serikali. Sasa najiuliza na kushangaa. Ni serikali gani iliyokuwa 'ipinduliwe' wakati uchaguzi wa kuchagua watakaounda serikali na mihimili yake ndo walikuwa bado kuchaguliwa? Huu ni ujanja au uzwazwa wa watawala...

  14. JamiiForums Tanzania Hata Mungu hawezi vumilia huu uhalifu wa kutaka kuivuruga amani ya nchi

    Nimeona watu wengi wakitamka kuwa Mungu atalipa kwa yaliyotokea baada ya uhalifu uliofanyika. Mimi kama mkristo ninayeijua biblia vizuri niwakumbushe tu kuwa waliofanya uhalifu kuanzia siku ya uchaguzi ni kuwa Mungu pia hafurahishwi na huo upuuzi. Mungu hutoa adhabu kali sana kwa watu kama hao...
  15. A

    JamiiForums Tanzania Jelly Silaa amaliza ubunge 2025 kwa maumivu, aswekwa ndani akidaiwa kutaka kupindua matokeo.

    Miongoni mwa mawaziri wote wa Baraza la Mawaziri la 2020-2025, Jerry William Silaa peke yake ndiye waziri aliyeanguka ubunge hivyo kupoteza sifa ya kuteueliwa kuwa waziri tena kwenye baraza lijalo. Jerry Silaa aligombea ubunge 2025-2030 kwenye Jimbo la Ukonga, Ilala jijini Dar es Salaam kupitia...
    • Ambakucha
    • Thread
    • kupindua kutaka matokeo maumivu ndani silaa ubunge ubunge 2025
    • Replies: 9
    • Forum: Jukwaa la Siasa
  16. H

    JamiiForums Tanzania Je waTanzania waandamane kutaka bima ya Afya kwa wote au kupinga uchaguzini?

    Ni kweli mnaweza kuandamana hiyo 29.10.2025 ila ni hatari sana iwapo hauna bima ya afya kwani utahitaji matibabu baada ya kipigo na utaenda kutibiwa kwa gharama sana. Je,tuandamane kugomea uchaguzi au tuandamane kudai bima ya afya kwa wote!! Tujitafakari!

  17. JamiiForums Tanzania Kumbukizi: Bashe aliwahi kukemea utekaji na kutaka ukamataji ufuate utaratibu wa kisheria

  18. JamiiForums Tanzania Kwanini CCM wanaidharau na kutaka kuikomoa Arusha?

    Kwa wanaojua namna wana Arusha wanavyojitambua na walivyo na historia ya kuchagua upinzani ukiondoa mwaka 2020 ambapo Magufuli aliwafanyia ujambazi, anashangaa maana na mantiki ya CCM kuweka Daudi Albert Bashite kama mgombea wao. Sidhani kama anaweza kupata kura hata moja kama kura...
  19. W

    JamiiForums Tanzania Wananchi kuwasha moto mitaani kwenye Maandamano Ufaransa ya kutaka Rais Macron ajiuzulu

    Zaidi ya watu 200,000 wameandamana na mamia wakamatwa nchini Ufaransa Septemba 11, 2025 kufuatia maandamano makubwa ya kitaifa yaliyoanza Septemba 10, 2025 wananchi wakipinga mipango ya kupunguza bajeti na hali tete ya kisiasa nchini humo. Vuguvugu hilo lililopewa jina “Fungeni Kila Kitu”...
    • Wild Flower
    • Thread
    • kujiuzulu kutaka maandamano macron mitaani moto rais rais macron ufaransa wananchi
    • Replies: 24
    • Forum: International Forum

  20. JamiiForums Tanzania Suala la kufungiwa kwa makanisa na majukwaa pamoja na kuteka ni jaribio la kutaka kuiteka nchi

    Hivi vitu vyote utekaji, mauwaji, ubambikiwaji wa kesi, uhalifu kwa viongozi wa dini na kufungiwa kwa JamiiForums ni jaribio la kutaka kutoa vitisho ili waiteke nchi kila mtu hawaogope. Sasa kuna wahaini wanajaribu kujimilikisha hii nchi wanajaribu kupata control ya kila kitu, nchi bado haija...
    • Genius Man
    • Thread
    • jaribio kufungiwa kutaka majukwaa makanisa nchi pamoja suala
    • Replies: 0
    • Forum: Jukwaa la Siasa
Menu
Log in
Register
Cookies are required to use this site. You must accept them to continue using the site. Learn more…