Question

A=1+6+6²+...+6¹⁰¹ este divizibil cu 7×37×43​

Answer 1

A=1+6+6²+...+6¹⁰¹

Grupam convenabil termenii:

$A=(1+6)+6^2(1+6)+6^4(1+6)+...+6^{100}(1+6)\\\\A=7(1+6^2+6^4+...+6^{100} \ divizibil\ cu \ 7$

$A=(1+6^2)+(6+6^3)+(6^4+6^6)+(6^5+6^7)+...+(6^99+6^{101})\\\\A=37+6(1+6^2)+6^4(1+6^2)+6^5(1+6^2)+...+6^{99}(1+6^2)\\\\A=37(1+6+...+6^{99})\ divizibil\ cu\ 37$

$A=(1+6+6^2)+6^3(1+6+6^2)+...+6^{99}(1+6+6^2)\\\\A=43(1+6^3+...+6^{99})\ divizbil\ cu\ 43$

Un alt exercitiu gasesti aici: https://brainly.ro/tema/146958

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