Question

b)a+b=115 și (a,b)=23.
Repede am nevoie urgent,vă rog frumos!!!​

Answer 1

a) (a,b)=5 => a=5k, unde k €N

b=5p, unde p €N, iar (k,p)=1

a+b=35 <=> 5k+5p=35 <=> k+p=7

Daca k=0 => a=0, b=35, (0,35)=35 nu convine

k=1 => a=5, b=30, (5,30)=5 convine

k=2 => a=10, b=25, (10,25)=5 convine

k=3 => a=15, b=20, (15,20)=5 convine

k=4 => a=20, b=15, (20,15)=5 convine

k=5 => a=25, b=10, (25,10)=5 convine

k=6 => a=30, b=5, (30,5)=5 convine

k=7 => a=35, b=0, (35,0)=35 nu convine

b) (a,b)=23 => a=23k, unde k € N

b=23p, unde p € N, iar (k,p)=1

a+b=115 <=> 23k+23p=115 <=> k+p=5

Daca k=0 => a=0, b=115, (a,b)=115 nu convine

k=1 => a=23, b=92, (23,92)=23 convine

k=2 => a=46, b=69, (46,69)=23 convine

k=3 => a=69, b=46, (69,46)=23 convine

k=4 => a=92, b=23, (92,23)=23 convine

k=5 => a=115, b=0, (115,0)=115 nu convine