a si b ∈N; a<b
a ) (a,b) = 14 si a + b = 112
a=14m si b=14n; (m;n)=1
a+b=14m+14n
14(m+n)=112 |:14
m+n=8 si a<b => (m;n)={(1;7); (3;5)}
=> (a;b)={(1•14; 7•14); (3•14 ; 5•14)}
(a;b)={( 14; 98); (42 ; 70)}
b) (a,b) = 18 si a × b = 1620
a=18m si b=18n; (m;n)=1
a•b=18m•18n
324•m•n=1620 |:324
m•n=5
=> m=1 si n=5
a=1•18 si b=5•18
a=18 si b=90
