Some numbers have special divisibility. For example, a number divisible by 1 1 can be divisible by 1 1 (or ten times because1=10). For example, 12 1,1=1,1 1 can be 1 1. This method is proved well for 1 1, but not necessarily for others. (A double-tailed number is actually a multiple of 1 1, and the remaining numbers are divided by1no matter how many degrees of1). Therefore, if the remainder can be divisible by 1 1, it is enough to explain the original number.

Another example is that 13 is the fourth (or ninth) tail, 17 is the fifth (or 12) tail, and 19 is the second (or 17) tail. ...

So what is the law between them?

Also, for example. The variational method (German pupil method, also known as multi-digit root method) is roughly like this: for example, 169 divided by 13 equals 13, 1+6+9 = 16,1+3 = Then it's 65438. The most extensive application of this method is to check whether the result of complex mixing operation is correct. Simply put, the method of changing one is actually to repeat the summation process of a certain number until it is converted into a number less than 10. For example, if123156:1+2+3+4+5+6 = 2+1= 3, then the number obtained by replacing 123456 with one is 3. However, division must be converted into multiplication. ) After dealing with the multiples of 13 with four tails, it is found that they have a regression: 26 or 26(6 times 4 plus 2), 39 or 39, and 52 becomes 13. 7 10, 13 and other numbers will become13; Change the number to 12, 15, etc. Get 39. Then 8,11...; 7, 10, 13……; 12, 15 ... each became arithmetic progression.

Later, after research, it was proposed that the correlation of 1 1 can also be explained as follows:

For an N-digit A, it is expressed as a= 10x+y, where Y is a digit, and X is n- 1 digit after A minus one digit Y (for example, A is 12 1, Y is 1, and X is. )

a = 10x+Y = 1 1x-(x-Y)。 Obviously, as long as X-Y is divisible by 1 1, A can be divisible by1. (For example, A is 12 1, Y is 1, and x-y is12-1=1).

This method can be extended to this kind of problem, such as the proof of 13:

a = 10x+y = 13x+ 13y-3x- 12y = 13(x+y)-3(x+4y)；

Or a =10x+y =13x-26y-3x+27y =13 (x-2y)-3 (x-9y).

The above similar problems are solved one by one.