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SEAMO 2027 - Paper F - SET 09 - Self-study Question 20

SEAMO · SEAMO 2027 - Paper F - SET 09 - Self-study

Question 20

A sequence has terms divisible by 3, each one being a square number minus 1:
$$3,15,24,48,63,\ldots.$$
Find the remainder when its 2018th term is divided by 1000.

Sequence convention for self-study: list all positive integers satisfying the two properties in strictly increasing order, with no omissions, as indicated by the displayed initial terms.