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!