MathDB

A palindrome in base

b

is a positive integer whose base-

b

digits read the same backwards and forwards; for example,

2002

is a

4

-digit palindrome in base

10

. Note that

200

is not a palindrome in base

10

, but it is a

3

-digit palindrome:

242

in base

9

, and

404

in base

7

. Prove that there is an integer which is a

3

-digit palindrome in base

b

for at least

2002

different values of

b

Problem Statement