Question

Determinati numerele prime a, b si c, diferite doua cate doua, stiind ca:
a+2b+4c=36

*Coronita*

Answer 1

a. a+2b+4c=36⇒36-numar; 4c-numar ,c∈N⇒2b-numar par ,b∈N⇒a-numar par⇒a-numar prim;
⇒a=2;
⇒2+2b+4c=36
⇒2b+4c=34⇒4c<34⇒c=[2,3,5,7]⇒patru variante;
⇒c=2⇒2b+8=34⇒2b=26⇒b=13⇒numar prim;
⇒c=3⇒2b+12=34⇒2b=22⇒b=11⇒numar prim;
⇒c=5⇒2b+20=34⇒2b=14⇒b=7⇒numar prim;
⇒c=7⇒2b+28=34⇒2b=6⇒b=3⇒numar prim;
b=[3,7,11,13]⇒patru variante;⇒a≠b≠c⇒a=2⇒c=5⇒b=7;
b. 3a+16b=54⇒54-numar par; 16b-numar par ,b∈N; 3a-numar par⇒a=2⇒numar prim par;
⇒6+16b=54⇒16b=48⇒b=3⇒numar prim impar;