Răspuns:
a=2, b=2, c=2, d=3
Explicație pas cu pas:
a+2b+4c+8d=38, a,b,c,d numere prime
a=38-(2b+4c+8d)
a=38-2(b+2c+4d)
a=2(19-b-2c-4d) ⇒ a numar par; dar a numar prim ⇒ a=2
2+2b+4c+8d=38
2b+4c+8d=36
2(b+2c+4d)=36
b+2c+4d=18
b=18-2(c+2d)
b=2(9-c-2d) ⇒b numar par; dar b numar prim ⇒b=2
2+4+4c+8d=38
4(c+2d)=32
c+2d=8
c=2(4-d) ⇒ c numar par; dar c numar prim ⇒c=2
2+4+8+8d=38
14+8d=38
8d=24
d=3