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

    JamiiForums Tanzania Kufananisha mafuriko ya Rufiji na yanayotokea sehemu nyingine ya nchi ni kutaka kuficha udhaifu wa viongozi na watendaji

    Nimeona sasa baada ya mafuriko (na si mafuriko bali "maji kujaa ktk Barabara na majengo yaliyo kando") baadhi ya watu wameona kuwa hilo ndilo jibu la mafuriko ya Rufiji. Ukweli ni kwamba mafuriko ya Rufiji kamwe hayawezi kuwa sawa na mengine kwa sababu, 1. Ukubwa wa mafuriko na eneo kubwa...
    • Mbogi
    • Thread
    • kuficha kutaka mafuriko nyingine rufiji sehemu udhaifu viongozi watendaji
    • Replies: 26
    • Forum: Jukwaa la Siasa
  2. mwanamwana

    JamiiForums Tanzania Kahama: Bertha Mabula adai polisi kutaka kumbambikia kesi ya ugaidi kutaka kulipua Mahakama Kuu

    Bertha Mabula amesema anahofia usalama wake kwa madai ya kubaini Polisi Mjini Kahama wanataka kumbambikia kesi ya ugaidi wakidai alitaka kulipua Mahakama Kuu Kanda ya Shinyanga wakati akifuatilia mwenendo wa shauri lake kwa ajili ya kukata rufani. Bertha amedai alifika Mahakama Kuu kwa ajili ya...
  3. Nyamesocho

    JamiiForums Tanzania Huu ni aina ya utapeli au ni watu wamekosa kazi ya kufanya na wanaofanya haya wanataka nini? Labda kutaka kukukomoa sijui!

    Kuna watu wanakupigia simu eitha uwape namba ya dreva tax,bodaboda wakiomba huduma eneo fulani au Kama una namba zao uwapigie waende walipo hasa maeneo yanayotajwa ni yale wanayojua ulipo hayawezi kukosa,makanisa,shule,stendi,kiwanja cha mpira au soko Ukimwambia bodaboda au dreva tax nenda...
  4. The Dictator

    JamiiForums Tanzania Makonda: Kuna UJINGA unaendelea wa kumtofautisha Hayati Magufuli na Rais Samia

    Makonda katika sherehe za kuipokea ndege mpya ya ATCL (BOEING 737-9 MAX) jijini Dar; amekemea tabia inayoonekana kuanza kukua na kukomaa kwa baadhi ya viongozi wa Serikali kwa ngazi mbalimbali ya kujaribu kutenganisha mafanikio yanayoendelea kutokea chini ya Rais Samia na kipindi cha awamu ya...
    • The Dictator
    • Thread
    • dr magufuli hayati kinyume kutaka magufuli maji makonda samia ujinga
    • Replies: 173
    • Forum: Jukwaa la Siasa
  5. Webabu

    JamiiForums Tanzania Marekani yaacha kuiendekeza Israel. Yapeleka azimio UN kutaka vita vya Gaza visitishwe bila masharti yoyote

    Mfadhili mkubwa wa Israel,Marekani baada ya kuona madhara kwa pande zote ya vita vya Gaza,ghafla imebadili mwelekeo na kupeleka azimio baraza la usalama la Umoja wa mataifa linalotaka vita hivyo visitishwe haraka. Katika azimio lililopelekwa baraza hilo mwezi Februari kikwazo ilikuwa ni Marekani...
  6. Erythrocyte

    JamiiForums Tanzania Utawala wa Awamu ya 5 kulikuwa na kampeni ya wazi ya kutaka aliyekuwepo aongoze milele, Sababu hasa ya kampeni hii ilikuwa nini?

    Tunaendelea na nyuzi zetu za mwezi wa 3, ambao ni mwezi wa Mungu. Ni wazi kila mwananchi anafahamu kuhusu kampeni za wazi kabisa za kutaka Rais wa awamu ya 5 Dkt John Magufuli aongezewe muda wa utawala wake kinyume kabisa cha Katiba ya Tanzania, yaani baada ya kumaliza utawala wake wa miaka...
  7. sanalii

    JamiiForums Tanzania Mtaani kuna vibaka, serikalini kuna majambazi!

    1. Kama Mkuu wa Kituo cha PolisI anaweza shirikiana na wenzake wakaiba hela kisha wakamuua kabisa mtu, 2. Mfanyabiashara aliefariki "Kwa kujupiga risasi" anakwambia polisi alimpigia afisa wa TRA akimwambia "Njoo kuna deal kubwa", na afisa akaja akiwa kavaa pensi na ndala akiongozana na askari...
  8. G

    JamiiForums Tanzania Mafanikio kiduchu kelele kama zote, Kwanini watu wa Forex wanavimba sana na kutaka attention hata kwa mafanikio madogo?

    1. Mtu wa forex anaweza kuwa na laki 4 bank lakini akatumia laki 1 kupiga picha kali location kali, ni watu ambao wana undugu na photoshoot. 2. Wakinunua magari (gari pendwa mark x) wataweka maandishi ya forex, wengine wanaenda mbali kuweka plate number za milioni 10 kwenye gari zisizozidi...
  9. THE FIRST BORN

    JamiiForums Tanzania Tukio la kocha Wa Belouzidad kutaka kuzichapa na mchezaji wake, limenikumbusha tukio la Mohamed Hussein na Manula-Novemba 5

    Hii Yanga ipo siku itakuja ifanye watu wazima wazichape tena Live na camera za Azam tena watu wenye heshima zao kama wachezaji na kocha. Leo kocha alinyakua chupa akataka kumtwanga nalo mchezaji aliekua anaonekana ana mshutumu kocha kua yanayotokea pale uwanjan kosa ni yeye Hii imenikumbusha...
  10. Nsanzagee

    JamiiForums Tanzania Nani aliyesema mafisadi wanaweza kutaka kiongozi mwenye kuwadhibiti? Kati yao, nani atake tena kiongozi kama Magufuli?

    Siku zote fisadi ni kama mtu kipofu asiyeelewa wala kujua kama naye ni mtu wa kufa kama ilivyo kwa wengine Kazi kubwa kwao ni kuiba na kukusanya mali pasipo kujua uhalali wa makusanyo hayo, kwa bahati mbaya kabisa, hata wakiwa navyo vyote, bado watataka na kingine kutoka mahali popote na kwa...
    • Nsanzagee
    • Thread
    • kati kiongozi kutaka kuwadhibiti mafisadi magufuli nani tena
    • Replies: 47
    • Forum: Jukwaa la Siasa
  11. G

    JamiiForums Tanzania Akili za wanachuo wengi zimekaa kipigaji na kutaka zaidi ya mlichokubaliana ukiwaweka madukani, kwanini?

    Japo inategemeana mtu na mtu, kwa wastani Darasa la saba na form 4 wengi wala hawana shida ukiwaweka dukani, Shida inakuja uwaweke waliosoma vyuoni, yani hata awe kasomea kozi ya secretary ni shida sana, mwanzoni mnakubaliana vizuri kabisa mshahara, day allowance, muda wa kufika, n.k. lakini...
  12. BARD AI

    JamiiForums Tanzania Wakulima waandamana kutaka Waziri ajiuzulu, Bajeti ya Kilimo iongezewe

    BULGARIA: Wakulima wakubwa na Wadogo wameandamana kwa siku ya pili walishinikiza Serikali kuweka Uongozi Unaowajibika pamoja na kuongezwa kwa Fedha za Ruzuku ya Kilimo nchini humo. Kamati ya Mipango ya Wakulima hao imesema Umoja huo hautasitisha Maandamano hayo hadi Waziri wa Kilimo, Kiril...
  13. BARD AI

    JamiiForums Tanzania Mwenyekiti wa Kamati ya Ujenzi ya Shule afikishwa Mahakamani kwa kutaka kumhonga Afisa wa TAKUKURU

    TAASISI ya Kuzuia na Kupambana na Rushwa (TAKUKURU) mkoani Morogoro, imemkamata na kumfikisha mahakamani Mwenyekiti wa kamati ya ujenzi wa shule, Suleiman Mwishehe kwa tuhuma za kujaribu kumhonga Afisa wa TAKUKURU kwa kutoa shilingi Milioni 3 ili asifikishwe mahakamani wakati wa uchunguzi kwa...
  14. Peter Dafi

    JamiiForums Tanzania PreGE2025 Dkt. Emmanuel Nchimbi: Mkiwaona CHADEMA wanaandamana mjue wameamua kutumia miguu kufikiri

    Katibu Mkuu wa Chama cha Mapinduzi Balozi Nchimbi akizungumza na Wanachama na Wananchi wa Mkoa wa Dar es Salaan Leo amesema. Mkiwaona CHADEMA wana Andamana Mjue wameamua kutumia Miguu Kufikiri Badala ya Akili/Ubongo. https://www.instagram.com/reel/C2UvdMwtYtD/?igsh=ZWNpZmN3OW8wdHJq
  15. Shining Light

    JamiiForums Tanzania, JamiiForums Uganda Ashambuliwa na watoto wake baada ya kutaka kuuza ardhi ya familia

    Mwanaume mmoja mwenye umri wa miaka 50, Kanu Mugwere, ameshambuliwa na watoto wake wakipinga uamuzi wake wa kutaka kuuza ardhi ya familia kwa shilingi milioni 1.5. Kulingana na taarifa, Mugwere alikuwa akilenga kutumia fedha hizo kugharamia matibabu ya mtoto wake mmoja mwenye ugonjwa wa akili...
  16. GENTAMYCINE

    JamiiForums Tanzania Kwa Dhamira yao Ovu ya kutaka Kuivamia Israel ya Afrika (Rwanda) naona Tshisekedi na Ndayishimiye wamechoka Kuishi

    Nasikia kuna Rafiki yao Mwingine 'Taifa Nafiki Nafiki' la Afrika Mashariki nao Kisirisiri watakuwa Wanawasaidia Congo DR na Burundi katika Kuipiga Israel ya Afrika ( Rwanda ) ya Military and Intelligence Genius Rais Paul Kagame hivyo GENTAMYCINE nachukua nafasi hii Kuwaonya kwani hawatoamini kwa...
  17. M

    JamiiForums Tanzania Huyu nae ameshasahaulika. Kelele za kutaka kumtoa kifungoni na UwT CCM zilishapoa

  18. Webabu

    JamiiForums Tanzania Maandamano makubwa yafanyika Morocco kutaka kufutwa mahusiano na Israel

    Japokuwa Morrocco wamekuwa wakiandamana mara kwa mara dhidi ya Israel, lakini maandamano ya jana disema 24 ndiyo makubwa zaidi kufanyika kwa ajili ya kuitaka nchi yao kusitisha mahusiano yote yaliyokubaliwa mwaka 2020. Maandamano hayo yaliyosimamiwa na chama cha Kiislamu cha Al adl wal ihsan...
    • Webabu
    • Thread
    • israel kufutwa kutaka maandamano mahusiano makubwa morocco
    • Replies: 10
    • Forum: International Forum
  19. M

    JamiiForums Tanzania Yanga komaeni kushinda mechi zenu: Hii ndoto ya kutaka Al Ahly amfunge CRB ugenini ni ndoto ya bafuni wakiwa wanaoga!!

    Namna pekee (the only scenario) ya Yanga kutinga robo fainali ni ya kushinda mechi zake zote mbili zilizobaki dhidi ya CRB nyumbani na dhidi ya Al Ahly wakiwa ugenini! Kama ubavu huo hawana wasahau ndoto za kuingia hatua ya robo fainali!! Kama Al Ahly alishindwa kumfunga CRB akiwa nyumbani ni...
  20. Webabu

    JamiiForums Tanzania Oman yajiweka kimbelembele kutaka Houth waache kushambulia meli zipitazo bahari nyekundu

    Msemaji wa wanamgambo wa Houth amesema wapo Oman kwa mwaliko wa kuzungumza na upande mwengine wa kimataifa kwa ajili ya kuacha mashambulizi ya meli zinazopita mlango wa bahari wa Bab Mandeb. Mohamed Abdel-Salam hakutaja huo upande wa pili katika mazungumzo hayo lakini akasisitiza kuwa msimamo wa...

Our Community

Coming Soon

Regional Communities

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