Digit sums of multiples of 11
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Answered
Some multiples of 11 have an even digit sum.
For example-
7*11 = 77 and 7+7 = 14, which is even;
11*11 = 121 and 1+2+1 = 4, which is even.
Do all multiples of 11 have an even digit sum?
(Prove that they do or find the smallest that does not.)
Best answer
using 11 division test we know abcdef if divisible by 11
a + c+e+(b+d+f)=2(sum of even or odd places) + some multiple of 11 having less digits then abcdef.now suppose statement in question works till n digits where n is any number then it will work for n+1 digits we just prove it works when n =2 so i did it
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