Question Number 27888 by Rasheed.Sindhi last updated on 16/Jan/18
$$\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{are}\:\boldsymbol{\mathrm{distinct}}\:\boldsymbol{\mathrm{primes}}\:\mathrm{and} \\ $$$$\mathrm{x},\mathrm{y}\in\left\{\mathrm{0},\mathrm{1},\mathrm{2},…\right\}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{divisors}} \\ $$$$\boldsymbol{\mathrm{common}}\:\mathrm{to}\:\mathrm{the}\:\boldsymbol{\mathrm{numbers}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{y}}} \right) \\ $$$$\boldsymbol{\mathrm{and}}\:\left(\boldsymbol{\mathrm{a}}^{\boldsymbol{\mathrm{y}}} \boldsymbol{\mathrm{b}}^{\boldsymbol{\mathrm{x}}} \right)? \\ $$
Commented by prakash jain last updated on 16/Jan/18
$$\mathrm{2}^{\mathrm{min}\left({x},\mathrm{y}\right)+\mathrm{1}} \\ $$
Commented by Rasheed.Sindhi last updated on 16/Jan/18
$$\mathrm{Than}\Bbbk\mathrm{s}\:\mathrm{Sir}!\:\mathrm{Any}\:\mathrm{process}? \\ $$$$\mathrm{Why}\:\mathrm{2}\:\mathrm{is}\:\mathrm{involved}? \\ $$
Commented by Rasheed.Sindhi last updated on 17/Jan/18
$$\mathrm{Ok}\:\mathrm{Sir}! \\ $$
Commented by prakash jain last updated on 17/Jan/18
$$\mathrm{2}^{\mathrm{min}\left(\mathrm{x},\mathrm{y}\right)+\mathrm{1}} \:\mathrm{is}\:\mathrm{wrong}\:\mathrm{it}\:\mathrm{should} \\ $$$$\mathrm{have}\:\mathrm{been}\:\left(\mathrm{min}\left(\mathrm{x},\mathrm{y}\right)+\mathrm{1}\right)^{\mathrm{2}} . \\ $$
Answered by mrW2 last updated on 17/Jan/18
Commented by Rasheed.Sindhi last updated on 17/Jan/18
$$\mathrm{Quite}\:\boldsymbol{\mathrm{Ok}}\:\mathrm{Sir}!\:\mathcal{THANKS}-{a}-\mathcal{LOT}! \\ $$