Question

Ajutooor! vreau doar subpunctele b si c

Answer 1

b)

(a;b)=15
[a;b]=90
folosim relatia stiuta din clasa:
(a;b)[a;b]=ab
ab=15 x 90
ab=1350
(a;b)=15 ⇒ a=15m, b=15n cu (m;n)=1
ab=15m x 15n=1350
mn=6
m;n ∈N* deci se regasesc printre divizorii naturali ai lui 6.
m=1, n=6, a=15, b=90
m=2, n=3, a=30, b=45
m=3, n=2, a=45, b=30
m=6, n=1, a=90, b=15

c)
(a;b)=15
a+b=105
(a;b)=15 ⇒ a=15p, b=15k, cu (p;k)=1
a+b=15p+15k=15(p+k)=105
p+k=7
p=1, k=6, a=15, b=90
p=2, k=5, a=30, b=75
p=3, k=4, a=45, b=60
p=4, k=3, a=60, b=45
p=5, k=2, a=75, b=30
p=6, k=1, a=90, b=15