Question

数学。题目如图。

Answer 1

(7n+19)/(2n+1)

=(6n+3+n+16)/(2n+1)

=(6n+3)/(2n+1)+(n+16)/(2n+1)

=3+(n+16)/(2n+1)      只要(n+16)/(2n+1)是整数即可.

令(n+16)/(2n+1)=a

n+16=a(2n+1)

n+1/2+31/2=a(2n+1)

a(2n+1)-(2n+1)/2=31/2

(2n+1)(a-1/2)=31/2

31/2=1*(31/2)=31*(1/2)

1.   2n+1=1   n=0      不符合题意,舍去；

2.  2n+1=31   n=15     代入得

(7*15+19)/(2*15+1)

=(105+19)/(31)

=124/31

=4

所以n=15

Answer 2

(7n+19)/(2n+1)
=(7n+3.5+15.5)/(2n+1)
=(7n+3.5)/(2n+1)+15.5/(2n+1)
=3.5+15.5/(2n+1)
由于上式值为整数，所以15.5/(2n+1)的结果必为k+0.5(k为整数)
即15.5/(2n+1)=k+0.5
等号两边同乘以2，得31/(2n+1)=2k+1
由于31是质数，所以31=1*31，
2n+1=1或2n+1=31
n=0 或 n=15

Answer 3

Answer 4

啊，如果是我的话，我直接试出来的 难道要写过程啊