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Harvard-MIT Math Tournament

Algebra Difficulty 4.1 AIME Find the answer United States

Problem:
Express, as concisely as possible, the value of the product
$\left(0^{3}-350\right)\left(1^{3}-349\right)\left(2^{3}-348\right)\left(3^{3}-347\right) \cdots\left(349^{3}-1\right)\left(350^{3}-0\right)$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:
0 . One of the factors is $7^{3}-343=0$ , so the whole product is zero.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.