Question Number 122646 by mathocean1 last updated on 18/Nov/20
$${Determinate}\:{the}\:{couples}\: \\ $$$$\left({a};\:{b}\right)\:{such}\:{that}\: \\ $$$${GCD}\left({a};{b}\right)+{LCM}\left({a};{b}\right)={a}+{b} \\ $$$${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$$${LCM}:\:{least}\:{common}\:{multiple} \\ $$
Commented by mathocean1 last updated on 18/Nov/20
$${so}\:{we}\:{have}\:{m}\:{couples}\:{sir}? \\ $$
Commented by mr W last updated on 18/Nov/20
$${a}={p}_{\mathrm{1}} {p}_{\mathrm{2}} ...{p}_{{m}} \:{with}\:{p}={any}\:{prime}\:{number} \\ $$$${b}={p}_{\mathrm{1}} ^{{n}_{\mathrm{1}} } {p}_{\mathrm{2}} ^{{n}_{\mathrm{2}} } ...{p}_{{m}} ^{{n}_{{m}} } \\ $$$${gcd}\left({a},{b}\right)={a} \\ $$$${lcm}\left({a},{b}\right)={b} \\ $$
Commented by mr W last updated on 18/Nov/20
$${infinite}\:{couples}! \\ $$
Commented by mathocean1 last updated on 18/Nov/20
$${ok}\:{sir} \\ $$$$ \\ $$