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. Mystery

    JamiiForums Tanzania Mama Salma Kikwete, kutaka wake wa viongozi wakuu wapewe pension ni kumkufuru Mungu!

    Kwa kweli nilishtushwa Sana niliposikia mama Salma Kikwete, akilitumia Bunge la Jamhuri ya Tanzania, badala ya kuongelea Shida za watu wa Jimbo lake la Mchinga, anaongelea mambo yake binafsi. Eti anataka yeye kama mke wa Rais mstaafu, naye alipwe pension! Hivi hawa viongozi wa CCM wanatuonaje...
    • Mystery
    • Thread
    • kikwete kutaka maombi mungu viongozi wake wakuu
    • Replies: 131
    • Forum: Jukwaa la Siasa
  2. venchwa

    JamiiForums Tanzania Irene mnigeria nisamehe Nimekupa mimba bila kutaka ni bahati mbaya

    Kama kawaida yetu wanaume! Kuna muda nilisema nimestaafu lakin mmm hakuna kustaafu Unakutana Na mtoto hadi unachanganyikiwa , Mwezi wa 2 nikiwa hapa jijini changi nikapita Hotel inaitwa Indulge Urbun Nikamuona demu Mrembo Sana yan ! Ni mnigeria nikaanza kumlia timing, Ilikuwa Jumapili...
  3. Comred Mbwana Allyamtu

    JamiiForums Tanzania Mwaka mmoja bila Magufuli na legacy yake

    Kesho ni kumbukumbu ya kutimiza mwaka 1 toka Raisi wa 5 wa Tanzania John Pombe Magufuli alipo fariki dunia, Magufuli alikuwa ni M-Socialist wa mlengo mkali wa Shoto na mwanamagauzi mkubwa wa uchumi. Ni yeye Magufuli ambaye ameacha legacy kubwa sana Tanzania ya vitu ambavyo ni alama ya uongozi...
  4. Robert Heriel Mtibeli

    JamiiForums Tanzania Moja ya Dalili ya Kiongozi Mpumbavu ni kutaka kuogopwa.

    Wakuu Kwema! Leo sina mengi Sana ya kusema, Mtoto wangu aliniuliza hivi; Baba ni Dalili gani ya wazi itakayonifanya nimjue kiongozi huyu ni Mpumbavu ili nijiepushe naye? Swali lake linashangaza Sana. Ukizingatia yeye ni mtoto wa miaka sita tuu. Nikamjibu; Kiongozi Mpumbavu utamtambua Kwa...
  5. kmbwembwe

    JamiiForums Tanzania Rais samia, Magereza wanaovutana kwenye miradi kushirikiana na sekta binafsi ni kutaka kulea upigaji

    Rais samia hua anatoa kauli na maelekezo yenye utata. Lakini wenye kuelewa wanajua ni mwelekeo wake wa kupendelea sekta binafsi iliyojaa 'wahuni' Inafaa atambue sekta binafsi kuleta ufanisi inatakiwa kua shindani sio kubebwa kwa kusudi kuingia ubia na majeshi au mashirika au mamlaka za umma...
    • kmbwembwe
    • Thread
    • binafsi kulea kushirikiana kutaka magereza miradi rais rais samia samia upigaji
    • Replies: 11
    • Forum: Jukwaa la Siasa
  6. D

    JamiiForums Tanzania Je, ikiwa Mrusi na Mchina wakiungana kijeshi kutaka kum-maliza Mmarekani kivita itachukuwa muda gani?

    Hili ni swali ambalo nimekutana nalo mahala fulani na mmoja wa wachangiaji ambaye ni Mr Kyle Krebs ambaye ni B.S. in Electrical Engineering & Mathematics, The University of Utah anajibu kama ifuatavyo: 1. Hawataweza kufika kwenye Mainland kwa sababu Mmarekani ana madude kama haya 11 USS...
  7. S

    JamiiForums Tanzania Waziri Mkuu wa Sweden akataa wito wa upinzani wa kutaka Sweden ijiunge NATO, asema hilo litaleta machafuko na kuharibu amani

    Waziri Mkuu wa Sweden Magdalena Andersson amekataa wito wa upinzani wa kuitaka Sweden kufikiria jambo la kujiunga NATO. Waziri Mkuu huyo amesema kufanya maombi ya kujiunga NATO kwa sasa kutaleta taharuki zaidi ktk eneo la Europe na kuhatarisha amani zaidi. Sweden kwa mara ya mwisho ilikuwa...
  8. N

    JamiiForums Tanzania Mbowe alilalamika 2018 kutaka kubambikiwa kesi

    Kama vile lissu alipolalamika kwamba kuna plans za kumuuua na baadaye akapigwa risasi za kutosha basi march 2018 mbowe alishayajua pia
  9. GENTAMYCINE

    JamiiForums Tanzania Nitashangaa sana kuwaona wale 'Natural Failures' 70 waliokosa 'Uteuzi' wa 'Uspika' wakigeukia tena kutaka Kugombea 'Unaibu Uspika' wa Bunge

    Hivi 'logically' tu kama dhamira na dhamiri yako Kuu ilikuwa ni kuwa Spika wa Bunge inawezekana ukabadilika na sasa Kuutaka Unaibu Uspika ambao haukuwa Chaguo lako la Moyoni? Ushauri wangu wa bure tu GENTAMYCINE Kwenu nyie 'Natural Failures' mpatao 70 ambao Dada na mwana Simba SC Mwenzangu Dk...
    • GENTAMYCINE
    • Thread
    • bunge kugombea kutaka sana tena uspika wa bunge uteuzi waliokosa
    • Replies: 20
    • Forum: Jukwaa la Siasa
  10. M

    JamiiForums Tanzania Rais Samia usikubali. CCM walikataa Katiba leo wanataka Katiba Mpya, walidhani Katiba ni ya CHADEMA tu

    Leo maji yamewafika shingoni wanakosa jinsi ya kukutoa madarakani wanaanza kujipitisha huku wakisema katiba mpya inahitajika, walidhani mfumo dume utadumu milele hawakujua mungu ndiye apangae. Sasa hivi wa CCM wanaumizwa na katiba kuliko wana Chadema.
  11. B

    JamiiForums Tanzania Tulitumia Bunge kutaka kufuta vyama vya siasa matokeo yake vyama vimeimarika Bunge limekufa

    Kazi Bunge nikuisimamia Serikali iliyopo madarakani itende Kwa maslahi ya Taifa. Kazi hii imegeuka siyo main objective tena bali lengo kuu la bunge lililopo chini ya uongozi wa sasa na ujao nikushirikiana na Serikali. Kushirikiria maana rahisi nikutengeneza pertnership na kwenye partnership...
  12. Action and Reaction

    JamiiForums Tanzania Simba SC haijawahi kutaka kumwacha Messi wa Msimbazi a.k.a Sakho

    Napenda kuliweka wazi swala hili baada ya kuona watu na wachambuzi wengi wakidai Simba SC ilitaka kumwacha Sacko sababu ya majeruhi! Ukweli ni kwamba wachambuzi wetu wa Bongo ndio wanafiki, washindiliaji na wahamasishaji tena wachonganishi....... etii Sacko hanauwezo, mara kiwango chake...
  13. S

    JamiiForums Tanzania Issue kubwa ni watu kutaka kutimiza ndoto zao za urais 2025 baada ya Mwendazake kuondoka

    Yatasemwa mengi na mtasikia mengi, ila issue kubwa ni watu kuutaka urais wa nchi hii mwaka 2025. Wakati Magu yuko hai, walikosa ujasiri wa kuonyesha hadharani mtatamani yao na kwa Mama, bado hawajaanza, ila ili wapate hiyo fursa(waanze) ni lazima Mama asigombee (bahati mbaya alishasema...
    • Salary Slip
    • Thread
    • baada kubwa kufariki kuondoka kutaka kutimiza ndoto magufuli mwendazake ndoto
    • Replies: 52
    • Forum: Jukwaa la Siasa
  14. I

    JamiiForums Tanzania Hii ni proof kuwa bila Marekani maisha hayawezekani

    Angalia jana insta, whatsap na facebook ilivyopotea na watu tukapoteana kabisa. Tusijaribu kuwaita mabeberu mana wameshikilia maisha yetu na imawezekana walifanya hivyo ili waone how do we value them. Hata case ya Mbowe wakiamua kumwambia samia amtoe gerezani fasta anamtoa vinginevyo wanamute...
  15. Kipenzi Changu

    JamiiForums Tanzania Mizengo Pinda: Tuanze mchakato wa kuwa na Tume huru ya Uchaguzi

    "Kuna mambo ambayo sisi CCM kama chama tawala lazima tubebe dhima. Tutoe uongozi. Kwa, mfano hili la Tume Huru ya Uchaguzi kizuizi ni nini? Hili ni jambo ambalo lazima tukubaliane na wenzetu wa upinzani na tuanze mchakato wa kuwa na Tume Huru ya Uchaguzi" Mzee Mizengo Pinda Hii inatoka...
    • Kipenzi Changu
    • Thread
    • huru katiba kupata kutaka mabadiliko ya katiba mchakato mizengo pinda mzee nje tuanze tume tume huru tume huru ya uchaguzi uchaguzi
    • Replies: 293
    • Forum: Jukwaa la Siasa
  16. Robert Heriel Mtibeli

    JamiiForums Tanzania Hakuna maisha magumu Zama hizi; kilichopo ni watu kutaka usawa

    HAKUNA MAISHA MAGUMU ZAMA HIZI, KILICHOPO WATU WA SASA KUPENDA USAWA. Kwa Mkono wa, Robert Heriel. Hakuna maisha rahisi Kama ya Zama hizi. Siku hizi kila kitu kimerahisishwa. Sijazaliwa zamani Sana Ila miaka ya 2000 Kurudi nyuma maisha yalikuwa complicated, yalikuwa magumu jamani. Sio kwenye...
  17. May Day

    JamiiForums Tanzania Naunga mkono Serikali kutaka Watoto wapumzike wakati wa likizo lakini....

    Mimi ni miongozi wa Wazazi nisiyefurahishwa kabisa na namna tunavyowachosha Watoto wetu kwa ratiba ngumu wakati mwingine kuliko hata tulizonazo sisi Watu wazima. Kuhusu likizo nadhani twaweza kuja na namna nyingine ya kwenda na Watoto wetu hawa bila kuendelea kuwaumiza...maana pia kama lengo...
  18. CM 1774858

    JamiiForums Tanzania EU kutaka kesi ya Freeman Mbowe ifutwe hawajui kuwa Tanzania is a free State?

    Tanzania ni nchi huru tena Uhuru wake ni wa miaka sitini (60) sasa Tanzania kama zilivyo nchi nyingine za EU inayo sheria,kanuni na taratibu za kuongoza watu wake ili waishi na kujiletea maendeleo yao kwa amani na Utulivu Freeman Mbowe na wenzake wanatuhumiwa kutenda kosa la Ugaidi na kesi...
  19. Rais wa Matajiri

    JamiiForums Tanzania Shaka: Ikitokea kuna dalili za Uhuru wetu kutaka kuwekwa rehani na sisi tukakaa kimya tusishangae makaburi ya wasisi wetu yatakapotetemeka

    == "Kazi ya kulinda tunu ya uhuru na Mapinduzi matukufu ya Zanzibar ni jukumu la kufa na kupona kwa kila mzalendo kwani fatiki ya kupigania uhuru imepoteza maisha na mali za watu, nguvu na jasho jingi" Shaka Mwenezi Taifa "Urithi wa Uhuru unapaswa kuthaminiwa na watanzania wote ambao ni...
  20. Sema Kimeumana

    JamiiForums Tanzania Chanjo ya UVIKO-19: Wasiotaka kuchanjwa wafunguliwe kesi ya kutaka kujiua

    Wadau, Dunia sasa linaingia katika wimbi la nne (fourth wave) ya maambukizi ya korona, kama tunavyosikia na kuona kupitia vyombo vya habari vya kimataifa, Ujerumani maambukizi yamefikia takriban 52,000+ ndani ya masaa 24 ambacho ni kiwango kikubwa ukilinganisha na waves zilizopita huko nyuma...

Our Community

Coming Soon

Regional Communities

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