Question

calculati ultima cifra a numarului 2 la puterea S + 5 la puterea S - 4 la puterea S unde S=3+6+9+...+99
URGEEENT

Answer 1

S=3+6+9+...+99=3(1+2+3+...+33)=3×33×34/2=1683
2¹⁶⁸³   ultima cifra  8
1683:4=420 si rest 3    deci 2³ = 8
5¹⁶⁸³    ultima cifra   5
4¹⁶⁸³    ultima cifra    4
1683:2=841 si rest 1    deci 4¹ = 4
ultima cifra a nr  2¹⁶⁸³  +5¹⁶⁸³ - 4¹⁶⁸³  ⇒ 8+5-4 = 9