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Solve-in-N-2-a-a-2-b-2-4704-GCD-a-b-7-b-13GCD-a-b-2SCM-a-b-4-3-lt-GCD-a-b-lt-7-GCD-greatest-common-divisor-SCM-smallest-common-multiple-




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

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