Question

P= 3^n x 5^n + 2 x 15^n+1 se divide cu 31, oricare ar fi n€N
Q=14^n+1 + 2^n x 7^n+2 se divide cu 9, oricare ar fi n€N

Answer 1

P=3ⁿ×5ⁿ+2×15ⁿ⁺¹

P=15ⁿ+2×15ⁿ×15

P=15ⁿ+30×15ⁿ

P=15ⁿ×(1+30)

P=15ⁿ×31⇒ P se divide cu 31

Q=14ⁿ⁺¹+2ⁿ×7ⁿ⁺²

Q=14ⁿ×14+2ⁿ×7ⁿ×7²

Q=14ⁿ×14+14ⁿ×49

Q=14ⁿ×(14+49)

Q=14ⁿ×63

Q=14ⁿ×7×9⇒ Q se divide cu 9