p-q-P-m-n-0-1-2-How-many-pairs-are-there-whose-LCM-is-p-m-q-n-when-i-a-b-amp-b-a-are-considered-same-ii-a-b-amp-b-a-are-considered-different-Generalization-of-Q-34358-

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Question Number 34385 by Rasheed.Sindhi last updated on 05/May/18

$$\mathrm{p},\mathrm{q}\in \mathbb{P}$$$$\mathrm{m},\mathrm{n}\in \{0,1,2,\dots \}$$$$\mathrm{How}\mathrm{many}\mathrm{pairs}\mathrm{are}\mathrm{there},\mathrm{whose}$$$$\mathrm{LCM}\mathrm{is}{\mathrm{p}}^{\mathrm{m}}{\mathrm{q}}^{\mathrm{n}},\mathrm{when}:$$$$\left(\mathrm{i}\right)(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{same}.$$$$\left(\mathrm{ii}\right)(\mathrm{a},\mathrm{b})\mathrm{\&}(\mathrm{b},\mathrm{a})\mathrm{are}\mathrm{considered}\mathrm{different}.$$$$\text{You can't use 'macro parameter character \#' in math mode}$$

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