Using the fact that 10≡−1(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 a0⋯an 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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