Question

Fie f:R f(x)=3x-2. Determinati a apartine N pentru care f(a)/a+1 este intreg

Answer 1

f(a)/(a+1) € Z
(3a-2)/(a+1) € Z
=> a+1 | 3a-2
a+1 | a+1 /•(-3)
=> a+1 | 3a-2
=> a+1 |-3a-3
____________+
a+1 | -5 => a+1 € D(-5)={-5,-1,2,5}
a+1=-5 => a= -6
a+1=-1 => a= -2
a+1=1 => a=0
a+1=5 => a=4
a € N
=> a € {0,4}