Question: [10 marks] When introducing Euclids algorithm in class, I made use of the following claim: Let d, u and v be positive integers. We have

[10 marks] When introducing Euclids algorithm in class, I made use of the following claim: Let d, u and v be positive integers. We have d|u and d|v if and only if d|v and d|(u mod v). Now prove this claim. Hint: Make sure to prove both the if and only if in this claim. The following identity mentioned in class is useful: u mod v = u vu/v

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