Ib kab zauv Qhov yooj yim tshaj plaws linear kab zauv Diophantine siv lub form ax + by=c, qhov twg a, b thiab c tau muab cov lej. Cov kev daws teeb meem tau piav qhia los ntawm cov theorem hauv qab no: Qhov kev sib npaug Diophantine muaj kev daws teeb meem (qhov twg x thiab y yog cov lej) yog tias thiab tsuas yog c yog ntau qhov sib faib loj tshaj plaws ntawm a thiab b.
Leej twg daws qhov sib npaug Diophantine?
Npe nyob rau hauv Honor ntawm 3rd-xyoo pua Greek mathematician Diophantus ntawm Alexandria, cov equations yog thawj systematically daws tau los ntawm Hindu lej pib nrog Aryabhata (c. 476–550).
Diophantine linear equation yog dab tsi?
A Linear Diophantine equation (LDE) yog ib qho kev sib npaug nrog 2 lossis ntau tus lej tsis paub thiab cov lej tsis paub yog txhua tus mus rau feem ntau ntawm 1. Linear Diophantine equation hauv ob qhov sib txawv yuav siv daim ntawv ax+by=c, qhov twg x, y∈Z thiab a, b, c yog cov lej tsis tu ncua.
Muaj pes tsawg txoj kev daws teeb meem Diophantine muaj pes tsawg leeg?
Hauv qhov piv txwv saum toj no, qhov kev daws teeb meem thawj zaug tau pom rau kab zauv Diophantine. Qhov no tsuas yog ib qho kev daws teeb meem ntawm qhov sib npaug, txawm li cas los xij. Thaum cov kev daws teeb meem muaj nyob rau ib qho kev sib npaug a x + b y=n, ax + by=n, ax + by=n, muaj tshwm sim ntau qhov kev daws teeb meem.
Koj paub li cas yog tias qhov sib npaug Diophantine muaj kev daws teeb meem?
Qhov kev sib npaug ntawm Diophantine yooj yim tshaj plaws siv daim ntawv ax + los ntawm=c, qhov twg a, b thiab c tau muab cov lej. Cov kev daws teeb meem tau piav qhia los ntawm cov theorem hauv qab no: Qhov kev sib npaug Diophantine muaj kev daws teeb meem (qhov twg x thiab y yog cov lej) yog thiab tsuas yog tias c yog ntau qhov sib faib loj tshaj plaws ntawm a thiab b
