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)
Енді ax + by + c = 0 теңдеуінің шешіміне келеміз, мұндағы (a, b) = 1. (8) қатынасты мына түрде жазамыз:
- =
Теңдіктің 2 жағын да өрнегіне көбейтеміз:
aQn-1 – bPn-1 = (-1)n
aQn-1 + b(-Pn-1) + (-1)n = 0
Шыққан теңдікті (-1)n-1 с с – санына көбейтеміз:
a [(-1)n-1 Qn-1] + b [(-1)n c Pn-1] + c = 0
осыдан келіп
x0 = (-1)n c Qn-1, y0 = (-1)n c Pn-1 (9)
теңдеудің шешімдері болады және теоремаға
сәйкес барлық шешімдері мына түрде жазылады:
x = (-1)n c Qn-1 - bt, y = (-1)n c Pn-1 + at,
мұндағы t = 0, 1, 2, ….
Шыққан нәтиже барлық 2 белгісізі бар бірінші дәрежелі теңдеулердің барлық бүтін шешімдерін табу туралы сұрақтың жауабын береді.
Достарыңызбен бөлісу: |