Question

am nevoie de ajutor
(a,b) = 11 si a + b + [ a,b ]
trebuie sa aflam a si b
(a,b) - c.m.m.d.c.
[ a,b ] - c.m.m.m.c

Answer 1

(a,b) = 11 si  a + b + [ a,b ]=121

(a,b)=11 => a=11m, b=11n; (m,n)=1; [a,b]=11•m•n

=> 11m+11n+11•m•n=121    :11

m+n+mn=11;

mn+m+n+1=12

m(n+1)+(n+1)=12

(n+1)(m+1)=2•6=3•4=4•3=6•2 si (m,n)=1

=> (m,n)={(1,5), (2,3), (3,2), (5,1)}

=> (a,b)={(11,55), (22, 33), (33,22), (55,11)}