Number theory proof verification requested

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Math100
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Homework Statement
Prove that ((a, b), b)=(a, b).
Relevant Equations
None.
Please view the picture of my work which I've uploaded.
 
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  • Handwritten proof on paper: Prove that ((a,b),b) = (a,b). Proof: Suppose (a,b) = k, then a = km and b = kn for some m, n in N, so ((a,b),b) = (k,b) and then (k,kn), since (k,kn) = k it follows that (k,kn) = (a,b), therefore ((a,b),b) = (a,b).
    Number Theory.jpg
    28.3 KB · Views: 162
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