MathDB

A positive integer is said to be palindromic if it remains the same when its digits are reversed. For example,

1221

74847

are both palindromic numbers. Let

k

be a positive integer that can be expressed as an

n

-digit number

\overline{a_{n-1}a_{n-2} \cdots a_0}

. Prove that if

k

is a palindromic number, then

k^2

is also a palindromic number if and only if

a_0^2 + a^2_1 + \cdots + a^2_{n-1} < 10

.
Proposed by Ho-Chien Chen

Problem Statement