Question Number 124688 by mathocean1 last updated on 05/Dec/20
$${Solve}\:{in}\:\mathbb{N}^{\mathrm{2}} : \\ $$ $${a}.\:\:\begin{cases}{{a}^{\mathrm{2}} −{b}^{\mathrm{2}} =\mathrm{4704}}\\{{GCD}\left({a};{b}\right)=\mathrm{7}}\end{cases} \\ $$ $${b}.\:\:\:\begin{cases}{\mathrm{13}{GCD}\left({a};{b}\right)−\mathrm{2}{SCM}\left({a};{b}\right)=\mathrm{4}}\\{\mathrm{3}<{GCD}\left({a};{b}\right)<\mathrm{7}}\end{cases} \\ $$ $$ \\ $$ $${GCD}:\:{greatest}\:{common}\:{divisor} \\ $$ $${SCM}:\:{smallest}\:{common}\:{multiple} \\ $$