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OPC 2 Problem 3

\(3. If \quad [a,b] = (a,b) . \text{ Then show that } a = \pm b.\) [a,b] means LCM. (a,b) means GCD.

Give different methods of solving this. This was a problem to the OPC 2. The OPC 2 has already ended. OPC 3 will be released soon.Calvin sir suggested me to do this.So Thanks to him.\(\ddot\smile\)

Note by Rajdeep Dhingra
2 years, 4 months ago

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This is easy. In fact

\[\left. (a,b) \right\vert a \left\vert [a,b] \right. = (a,b) \qquad \textrm{ where } \big\vert \textrm{ means } divides \]

This means \(a= \pm(a,b)\).

Same holds for \(b\), so \(a = \pm b\). Andrea Palma · 2 years, 3 months ago

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