There is a strange three digit number, which is exactly divided by 7 after subtracting 7, exactly divided by 8 after subtracting 8, exactly divided by 9 after subtracting 9______ ．

There is a strange three digit number, which is exactly divided by 7 after subtracting 7, exactly divided by 8 after subtracting 8, exactly divided by 9 after subtracting 9______ ．

Because this strange three digit is divided by 7, 8 and 9, so this three digit is the least common multiple of 7, 8 and 9, 7 × 8 × 9 = 504

In the positive integers from 1 to 2011, which numbers can be divided by 2, 5 and 8 at the same time, and what is the sum of which numbers
There is a detailed process

The numbers divisible by 2,5,8 are multiples of 40, 40 * 2,40 * 3 respectively So the sum of them is 40 * (1 + 2 + 3 +...) +50）=40*（1+50）*50/2=51000

Equation 0 = 1 / 4a-1 / 2B + C, 0 = 9 / 4A + 3 / 2B + C, - 5 = C

C = - 5
be
1/4a+1/2b-5=0
Double four on both sides
a+2b=20 (1)
9/4a+3/2b-5=0
9a+6b=20 (2)
(2)-(1)*3
9a-3a=20-60
6a=-40
a=-20/3
b=(20-a)/2=40/3
c=-5

A + B + C = 3 4A + 2B + C = - 2 4a-2b + C = 2

(2) (3), B = - 1 (4)
(4) Substituting (1), we get a + C = 4
(4) Substituting (2), we get 4A + C = 0
The solution is a = - 4 / 3, C = 16 / 3
So, a = - 4 / 3, B = - 1, C = 16 / 3