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Q: Subject: Linear Algebra
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Suppose a, b, and c are integers and suppose a | b and a - c, where a - c denotes
that c is not divisible by a. Prove that a - (b+c).
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- Let (a,b)=1. Prove that (a,bn)=1 for all positive integers n.Let and be positive integers. If and is the least common multiple of and , prove that . Note that it follows that the least common multiple of two positive relatively prime integers is their product.Let a,b,c and d be integers such that ab and cd. Prove that acbd.