Question

Determinati ultima cifra nenula a produsului
p=5la48*2la44*3la17

Answer 1

p = 5^48 × 2^44 × 3^17
Uc(p) nenula = ?

5^48 = 5^44 × 5^4

p = 5^44 × 2^44 × 5^4 × 3^17

p = 10^44 × 5^4 × 3^17

p = Uc(10^44) × Uc(5^4) × Uc(3^17)

Uc(10^44) = 0
cerinta cere ultima cifra nenula

Uc(5^4) = 5
Uc(3^17) = Uc(3^4×4+1) = Uc(3^1) = 3

deci,
Uc(p) nenula = (5 × 3) = Uc(15) = 5