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ripcity4545
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Homework Statement
Prove that every palindromic integer N in base 10 with an even number of digits is divisible by 11.
Then prove that every palindromic integer in base k with an even number of digits is divisible by k+1.
Homework Equations
palindromic means the number reads the same forwards and backwards
The Attempt at a Solution
I tried a general representation of a palindromic integer with even digits of form
D1*10^(2n-1) + D2*10^(2n-2) + ... +Dn * 10^n + Dn * 10^(n-1) +...+ D2*10^1 +D1*10^0
which makes the number N equal to
N= D1[10^(2n-1) + 10^0] + D2 [10^(2n-2) + 10^1] +...+Dn[10^n + 10^(n-1)].
But I can't figure out how to prove divisibility by 11. Thanks for any help!