<p>Find the number of ordered pairs of integers <img alt="$(a, b)$" height="18" src="https://latex.artofproblemsolving.com/2/8/e/28e24c43456d95b5ab8d4f2f8f85a644e98b7ed3.png" width="38" /> such that the sequence<img alt="\[3, 4, 5, a, b, 30, 40, 50\]" height="16" src="https://latex.artofproblemsolving.com/7/e/6/7e600c9592a3e3dd54485e84fa52b667f6c848b1.png" width="154" />is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.</p>

Question No: 432

Find the number of ordered pairs of integers $(a, b)$ such that the sequence $3, 4, 5, a, b, 30, 40, 50$ is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.

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Tags: Combinatorics Number Theory

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