Question

verifica daca sunt prime numerele: 3^40 + 2^42

Answer 1

U(3^1)=3
U(3^2)=9
U(3^3)=7
U(3^4)=1
................
U(3^40)=?

40:4=10

U(3^40)=U(3^{10·4})=U(3^4)=1



U(2^1)=2
U(2^2)=4
U(2^3)=8
U(2^4)=6
...................
U(2^42)=?

42:4=10 (rest 2)

U(2^42)=U(2^{4·10+2})=U(2^2)=4



U(3^40 + 2^42)=U(U(3^40)+U(2^42))=
=U(1+4)=U(5)=5


=> (3^40 + 2^42) divizibil cu 5
=> 3^40 + 2^42 nu e prim