Question

Aratati ca 2^990-1 se divide cu 21

Answer 1

2^990 – 1 = (3 – 1)^990 – 1 = M3 + 1 – 1 = M3
2^990 – 1 = (2^3)^330 – 1 = 8^330 – 1 = (7 + 1)^330 – 1 = M7 + 1 – 1 = M7
3 | 2^990 – 1 si 7 | 2^990 – 1  atunci 21 | 2^990 – 1