Now I have proved the following two problems:
(1) Prove that a number and the sum of its digits have the same remainder upon division by 9.
(2) Given an integer, consider the difference between the sum of the digits in odd positions (counting from the right) and those in even positions. Show that the difference has the same remainder as the number itself when divided by 11.
Then, I need help on the following problem:
Partition the digits of a number into groups of two and three, respectively, starting from the right. Treat these as two- and three-digit numbers, respectively, and proceed similarly as in the two problems above. What divisibility rules arise?
In fact, I did not quite get what this problem asks for and not clear about this process. Could anyone give me some hints on this, please?
Thanks in advance.
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