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2024 SSMO Team Round Problems/Problem 14

Problem

Let $a_1, a_2, \dots, a_7$ be the roots of the polynomial \[x^7+5x^6+9x^5+x^4+x^3+10x^2+5x+1.\] Find the value of \[\left|\prod_{n=1}^7 \prod_{m=n+1}^7 (a_na_m-1)\right|.\]

Solution

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