Question

2 la puterea 0 +.......2 la puterea 99 se divide cu 15

Answer 1

2^0=1
2^1=2
2^2=4
2^3=8                                      2+4+8+6=20
2^4=16 ultima cifra 6
2^5=32 ultima cifra 2

2^97= ultima cifra 97:4=24 rest 1  2=2
2^98= ultima cifra 98:4=24 rest 2  2^2=4
 
  0     1       2        3        99
2   +  2   + 2   +    2+....+2  =
         1        1          2         98
1+2 (1 + 2+ 2+..+2)

1+2[1+(24 cicluri deci de 20 ultima cifra 0)+2+4]=1+2(1+2+4)=1+2*7=15