A= 17
This problem is a redundancy problem and an extension of the congruence problem.
When positive integers A, B and C are divisible by the same positive integer D, the remainder is a multiple, so we say that positive integers A, B and C are greater than positive integers D.
There is a general solution to this kind of problem.
The remainder of positive integer A divided by positive integer D is positive integer B divided by positive integer D, and the remainder of positive integer B divided by positive integer D is positive integer C divided by positive integer D, so as to find a positive integer D..
Solution:
1, find the difference between a and B*E, and the difference between b and C*F, (greatly reduced), and then find the greatest common divisor m of these two differences, and list all common divisors of m;
2. Find the greatest common divisor n of A, B and C, and list all common divisors of n;
3. The divisors of all common divisors that are not the greatest common divisor m of the greatest common divisor n can be the values of d;
4. Verify these values and determine the correct values.
Example: There are three positive integers 603, 939 and 393 divided by the same number, and the remainder of 603 divided by this number is twice that of 939 divided by this number; The remainder of 939 divided by this number is twice that of 393 divided by this number. Find this number.
Solution:
939*2-603= 1275,939-393*2= 153,
( 1275, 153)=5 1=3* 17; 5 1 has four common divisors: 1, 3,17,51.
(603,939,393)=3。 3 has two common divisors: 1, 3.
Then the possible values of d are 17 and 5 1.
603/ 17=35……8,939/ 17=55……4,393/ 17=23……2。 Then 17 is the correct value of d.
603/5 1= 1 1……42,939/5 1= 18……2 1,393/5 1=7……36。 Then 5 1 is not the value of d.
So this number is 17.