AMO-Bench 2025 Problem 44

Let $a=\log_3\bigg(\frac{1}{2}\sum\limits_{n=0}^{676}(-1)^n{2028 \choose 3n}\bigg)$ . Calculate the sum of distinct prime factors of $a^2+(a-1)^4$ .

Dataset text AMO-Bench. Open licence.

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8281323

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