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  • https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT_310_Bridge_to_Advanced_Mathematics/04%3A_Direct_Proof/4.06%3A_Section_6-Exercises
    If a|b and a|c, then a|(b+c). If a2|b and b3|c, then a6|c. If a is an integer and a2|a, then a{1,0,1}. If nN and n2, then...If a|b and a|c, then a|(b+c). If a2|b and b3|c, then a6|c. If a is an integer and a2|a, then a{1,0,1}. If nN and n2, then the numbers n!+2,n!+3,n!+4,n!+5,,n!+n are all composite. (Thus for any n2, one can find n1 consecutive composite numbers. If a,b,cN and cba, then (ab)(ac)=(abc)(ab+cc).

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