Prove that is n is a positive integer such that the alternately adding and subtracting its digits in decimal representation yeilds divisible by 11 number, then n is divisible by 11.
Prove that is n is a positive integer such that the alternately adding and subtracting its digits in decimal representation yeilds divisible by 11 number, then n is divisible by 11.
Now
so:
That is is congurent to the number obtained by alternately adding and subtracting its digits in decimal representation, but is congruent to modulo , and therefore so is alternately adding and subtracting its digits in decimal representation.