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 integer constants. x thiab y tsis paub qhov txawv txav.
Diophantine sib npaug siv rau dab tsi?
Lub hom phiaj ntawm ib qho kev sib npaug Diophantine yog daws rau txhua qhov tsis paub hauv qhov teeb meem. Thaum Diophantus tab tom cuam tshuam nrog 2 lossis ntau dua qhov tsis paub, nws yuav sim sau txhua qhov tsis paub hais txog ib leeg xwb.
Qhov twg ntawm cov kab sib npaug Diophantine hauv qab no tsis muaj kev daws teeb meem?
Yog d tsis faib c, ces qhov linear Diophantine equation ax+by=c tsis muaj kev daws teeb meem.
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 suav Diophantine li cas?
Qhov yooj yim tshaj plaws linear Diophantine sib npaug yuav siv qhov 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.
