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palindrome in arithmetic sequence exists?

Source: VJIMC 1998 2.2

August 24, 2021
arithmetic sequencealgebranumber theorypalindrome

Problem Statement

Decide whether there is a member in the arithmetic sequence {an}n=1∞\{a_n\}_{n=1}^\infty whose first member is a1=1998a_1=1998 and the common difference d=131d=131 which is a palindrome (palindrome is a number such that its decimal expansion is symmetric, e.g., 77, 3333, 433334433334, 21353122135312 and so on).
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