Question

rezolvati in multimea nr. naturale ecuatia xy+y=6x+2017

Answer 1

y(x+1)=6x+2017
y=(6x+2017):(x+1)
y=(6x+6+2011):(x+1)
y=(6x+6):(x+1) +2011:(x+1)
y=6(x+1):(x+1) +2011:(x+1)
y=6+2011:(x+1) apartine nr. naturale
6 apartine nr nat
Deci trebuie sa demonstram ca 2011:(x+1) apartine numerelor naturale
pt a apartine numerelor naturale, x+1|2011
x+1€ divizorilor lui 2011
x+1€{1,2011}
x€{0,2010}