(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

palindromic means the number reads the same forwards and backwards

3. 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!

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# Divisibility by 11 for all palindromes with an even number of digits

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