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).
Hizi majuzi Papa Francis amelazimika kuomba radhi hadharani baada ya taarifa kuvuja kwamba kwenye kikao cha hivi karibuni na makadinali 250 wa Italia, Papa alitukana mashoga.
Kwenye kikao hicho binafsi Papa Francis alitumia maneno makali sana dhidi ya mashoga na ushoga. Zaidi Papa alionya...
Nyakati huja na nyakati hupita
Na nyakati ambazo huja na kupita, zingine huja kwa namna yake na changamoto zake, na zinapokuja, huja ili zibadilishe kitu na ama kuharibu kabisa,
Kikawaida, Ni mjinga tu ambaye hudhani Dunia haina Changamoto na kwamba anaweza kukaa maisha yake yote bila kupitia...
Wakuu, ukweli uko wazi CCM hawaitaki katiba mpya kwasababu ndio anguko lao la kiutawala, pia uwepo wa tume huru ndio msumali wa mwisho kwenye jeneza lao la utawala wa ulaghai.
Muungano huu ni feki na hauna faida kwa watanganyika zaidi ya kuwalalia na kuwanyonya, Kinana hajaweza kujibu hoja...
Wananchi wa kijiji cha Ndolezi kilipo kimondo maarufu cha Mbozi wamekuwa wakiishi hapo kabla ya wanasayansi kuthibitisha kuwa jiwe lile ni kimondo, hivyo kulipa jiwe hilo hadhi ya pekee kulinganisha na mawe mengine yaliyopo kijijini hapo.
Baada ya uthibitisho huo wanasayansi, watalii, na watu...
Uchambuzi wa ACT Wazalendo kuhusu mpango wa bajeti wa Wizara ya katiba na sheria kwa mwaka wa fedha 2024/25.
Utangulizi.
Tarehe 29 April 2024 Wizara ya katiba na sheria iliwasilisha hotuba ya bajeti kwa mwaka wa fedha 2024/2025. Bunge liliijadili na kuidhinisha kiasi cha Shilingi Bilioni...
salamu wanandugu,
Kama kichwa cha uzi .
Niliona video katika mitandao ya kijamii ikizunguka sana (viral video) ,ikimuonyesha Harmonize na Mwakinyo wakitishiana kupigana . Ila ukweli kabisa pale hakuna ngumi labda ni kick , hawakuwa serious.
Tuangalie kwanza mazingira waliyokutana. kama...
Kuna mambo hapa tanzania hususani hii biashara ya Forex imekuwa na majigambo mengi yani mtu ana kuonesha kapiga usd 5000 kwenye news kama CPI,NFP na n.k bado hapo hapo anaweka group au darasa la malipo watu walipie.
Au watu wa mikeka aka bettting
Kuna mashaka sana na hawa watu wa forex na betting
Habari wana JF poleni na Mvua kubwa zinazoendelea kunyesha kote Nchini
Kuna mdada amehamia katika Room inayofuatana na yangu sasa toka amehamia tunaishi poa sana kiasi hata nikiomba mzigo sahii ananipa.
Sasa juzi kamerudi kamelewa kakaniomba nikasaidie kufungua mlango wake sikustuka kumuona...
Mwanafunzi wa Mwaka wa Kwanza anayesoma Chuo Kikuu cha Dodoma (UDOM) ambaye jina lake halijawekwa wazi inadaiwa ametaka kufanya jaribio la kujiua akiwa chuoni hapo chanzo kikitajwa ni masuala ya mapenzi.
Inaelezwa kuwa tukio hilo limetokea jana Aprili 25, 2024 wakati alipokuwa katika moja ya...
Sisi Yanga huwa uwezo wa kuingia uwanjani wengi hawana. Mara nyingi mpaka iwe bure au kiwango cha chini sana. Sijajua ni utamaduni wetu au ni nini.
Simba wanapenda sana kwenda Uwanjani. This time naona sababu sisi ndo host ni kama wana kamgomo flani. Hawaoneshi kabisa nia ya kuja uwanjani. Na...
Kuna mtu ananielewa?
Ni kawaida kwa asili ya binadamu kutaka kuwa na hulka ya utimilifu na kutamani mazuri pekee.
Ndiyo maana katika maongezi yetu mara nyingi ni ligi na ushindani, hatuongei ili kusuluhisha bali tunajitetea kwa kuhakikisha tupo sahihi.
Matokeo yake ni vigumu mno kumaliza...
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...
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...
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...
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...
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...
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...
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...
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...
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...
JamiiForums uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.