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  • https://math.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame_IN/SMC%3A_MATH_339_-_Discrete_Mathematics_(Rohatgi)/Text/6%3A_Additional_Topics/6.E%3A_Additional_Topics_(Exercises)
    Assume ab and ac. This means that b and c are both multiples of a, so b=am and c=an for integers m and n. Then \(b+c = am+an = ...Assume ab and ac. This means that b and c are both multiples of a, so b=am and c=an for integers m and n. Then b+c=am+an=a(m+n), so b+c is a multiple of a, or equivalently, ab+c. Similarly, bc=aman=a(mn), so bc is a multiple of a, which is to say abc.

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