Question

[Lê Hoàng Bảo]

cho a=5^3+5^4+5^5+5^6+.....+5^32.Chung minh q chia het cho 6, cho 31

Answer 1

[Đoàn Đức Hà]

\(a=5^3+5^4+5^5+...+5^{32}\)

\(=\left(5^3+5^4\right)+\left(5^5+5^6\right)+...+\left(5^{31}+3^{32}\right)\)

\(=5^3\left(1+5\right)+5^5\left(1+5\right)+...+5^{31}\left(1+5\right)\)

\(=6\left(5^3+5^5+...+5^{31}\right)⋮6\)

\(a=5^3+5^4+5^5+5^6+...+5^{32}\)

\(=\left(5^3+5^4+5^5\right)+\left(5^6+5^7+5^8\right)+...+\left(5^{30}+5^{31}+5^{32}\right)\)

\(=5^3\left(1+5+5^2\right)+5^6\left(1+5+5^2\right)+...+5^{30}\left(1+5+5^2\right)\)

\(=31\left(5^3+5^6+...+5^{30}\right)⋮31\)