Divisor of fraction is divisor of numerator or denominator?If we have q ∣ x a – 1 x – 1 ,does that mean that q is divisor of x a – 1 or q is divisor of x − 1?

Question

Divisor of fraction is divisor of numerator or denominator?If we have  q  ∣                    x        a            –      1              x      –      1        ,does that mean that   q is divisor of       x    a    –  1 or   q is divisor of   x  −  1?

dasse9 · Accepted Answer

Divisibility is transitive. So if   a  ∣            b      c      , since             b      c        ∣  b (as             b      c        ⋅  c  =  b) we have   a  ∣  b

Leila Jennings · Accepted Answer

a      b      c      d              a      b        =  c  d since denominator   a  b divides   a  b  c  d then   c      |              a      b      c      d              a      b      . This means that   c is a divisor of the numerator.

Divisor of fraction is divisor of numerator or denominator? If we have q| (x^a – 1)/(x – 1), does that mean that q is divisor of x^a–1 or q is divisor of x−1 ?

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