Page "Coprime integers" Paragraph 10

As a consequence of the third point, if a and b are coprime and br ≡ bs ( mod a ), then r ≡ s ( mod a ) ( because we may " divide by b " when working modulo a ).

Furthermore, if b < sub > 1 </ sub > and b < sub > 2 </ sub > are both coprime with a, then so is their product b < sub > 1 </ sub > b < sub > 2 </ sub > ( modulo a it is a product of invertible elements, and therefore invertible ); this also follows from the first point by Euclid's lemma, which states that if a prime number p divides a product bc, then p divides at least one of the factors b, c.