2. In the book 1, 2, 3, ..., 1995, find all positive integers satisfying the following conditions.
A: (1995+a)| 1995a
Supplementary question: "|" means that the latter is divisible by the former.
Questioner: Peaches are crazy-the second best answer for trainee wizards.
1 is divisible by 72, that is, by 8 and 9.
Conditions that can be divisible by 8: the last three digits can be divisible by 8;
Conditions that can be divisible by 9: The number obtained by adding the digits of this number can be divisible by 9.
A number divided by 9 is equal to the sum of digits divided by 9.
This number is123456789112131415 ... 31323 3343533.
That is, write to 36.
2. let 1995a/( 1995+a)=b,
Factorization results in (1995+a) (1995-b) =19952.
And19952 = 32 * 52 * 72 *192.
If we make a < 1995, that is, 1995 2 is decomposed into two numbers, one of which is greater than 1995 and less than 1995+ 1995=3990.
There are several factors that can meet this requirement:
1995^2=2527* 1575
=3249* 1225
=3675* 1083
=2205* 1805
=2793* 1425
=3325* 1 197
At this time, the values of a are: 532, 1254, 1680, 2 10/0,798, 1330 respectively.