Palindromes and LCM A palindrome is a number that is the same when read forwards and backwards, such as $43234$. What is the smallest five-digit palindrome that is divisible by $11$?
I'm probably terrible at math but all I could do was list the multiples out. Any hints for a quicker solution?

$$\overline{abcba}\equiv 10^4\cdot a+10^3\cdot b+10^2\cdot c+10^1\cdot b+a$$
$$\equiv (-1)^4a+(-1)^3b+(-1)^2c+(-1)^1b+a$$
$$\equiv a-b+c-b+a\equiv 2a-2b+c\equiv 0\pmod{11}$$
To minimize $\overline{abcba}$, let $a=1$ and $b=0$. Then $c\equiv 9\pmod{11}$, so $c=9$. And in fact $\overline{10901}$ works.
