Saturday, 26 July 2014

number theory - Devise a test for divisibility of an integer by 11, in terms of properties of its digits

Using the fact that 101(mod11), devise a test for divisibility of an integer by 11, in terms of properties of its digits.




Approach:



Let the number with its digits a0an be represented as f(x)=a0xn++an. By exhaustion f(1)=0 if the number is divisible by 11, so f(10) is divisible by 11. Do I have to prove my conjecture? or it's trivial.

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