Question

aratati ca numarul D=7+7^2+7^3+.......+7^2004 se divide cu 57

Answer 1

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Answer 2

Grupam termenii cate 3 si dam factor comun convenabil.

$7(1+7+7^2) + 7^4(1+7+7^2)+7^7(1+7+7^2) + ... +7^{2002} (1+7+7^2)$

$7\cdot57+7^4\cdot57+ ...+7^{2002}\cdot57=57(7+7^4+7^7+ ... +7^{2002})\in M_{{57}}$