Question

[Nguyễn Thùy Duyên]

Chứng minh rằng: (7 + 7 mũ 3 + 7 mũ 5 + ....... + 7 mũ 1999 ) chia hết cho 35

Answer 1

[Nhóc_Siêu Phàm]

Ta có: A= 7×(1+7^2)+7^5×(1+7^2)+...7^1997×(1×7^2) A=7×50+7^5×50+...7^1997×50 A=350+7^4×350+...7^1996×350 A=35×10+7^4×35×10+...+7^1996×35×10 A=35×(10+7^4×10+...+7^1996×10) chia hết cho 35

Answer 2

[Nhóc_Siêu Phàm]

Ta có:

A= 7×(1+7^2)+7^5×(1+7^2)+...7^1997×(1×7^2)

A=7×50+7^5×50+...7^1997×50

A=350+7^4×350+...7^1996×350

A=35×10+7^4×35×10+...+7^1996×35×10

A=35×(10+7^4×10+...+7^1996×10) chia hết cho 35