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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 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 $$a = \pm b$$. · 2 years ago

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