Question

1. Chứng tỏ rằng:

B = 3 + 3³ + 3⁵ + ............. + 3¹⁹⁹⁵ + 3¹⁹⁹⁷ chia hết cho 13

2. Tổng, hiệu sau đây là số nguyên tố hay hợp số 

a, 31 . 37 . 39 . 43 + 61 . 53 . 55 . 59

b, 1999 . 20011 - 135786

Answer 1

Bài 1:

Ta có:

\(B=3+3^3+3^5+...+3^{1995}+3^{1997}\)

\(\Rightarrow B=\left(3+3^3+3^5\right)+...+\left(3^{1993}+3^{1995}+3^{1997}\right)\)

\(\Rightarrow B=3\left(1+3^2+3^4\right)+...+3^{1995}.\left(1+3^2+3^4\right)\)

\(\Rightarrow B=3.\left(1+9+81\right)+...+3^{1995}.\left(1+9+81\right)\)

\(\Rightarrow B=3.91+...+3^{1995}.91\)

\(\Rightarrow B=\left(3+...+3^{1995}\right).91⋮13\)

\(\Rightarrowđpcm\)

 

Answer 2

B=3+3³⁺35+.............+3¹⁹⁹⁵+3¹⁹⁹⁶

B= ( 3+3³+3⁵+3⁷+3⁹+3^{11) +.....+ (}3^1991+.....+3¹⁹⁹⁷⁾

^B= 3^{36+.... +}3^{36 :13}

hop so