Determinate the couples (a; b) such that GCD(a;b)+LCM(a;b)=a+b GCD: greatest common divisor LCM: least common multiple


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Question Number 122646 by mathocean1 last updated on 18/Nov/20

$D e t e r m i n a t e t h e c o u p l e s$ $(a; b) s u c h t h a t$ $G C D (a; b) + L C M (a; b) = a + b$ $G C D : g r e a t e s t c o m m o n d i v i s o r$ $L C M : l e a s t c o m m o n m u l t i p l e$
Commented by mathocean1 last updated on 18/Nov/20

$s o w e h a v e m c o u p l e s s i r ?$
Commented by mr W last updated on 18/Nov/20

$a = p_{1} p_{2} . . . p_{m} w i t h p = a n y p r i m e n u m b e r$ $b = p_{1}^{n_{1}} p_{2}^{n_{2}} . . . p_{m}^{n_{m}}$ $g c d (a, b) = a$ $l c m (a, b) = b$
Commented by mr W last updated on 18/Nov/20

$i n f i n i t e c o u p l e s!$
Commented by mathocean1 last updated on 18/Nov/20

$o k s i r$
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