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Problem 864

AMC 12 late, AIME early

Number theory Difficulty 4.6 Find the answer HMMT February

Compute the prime factorization of 1007021035035021007001.

Your answer

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

Official solution

The number in question is $\sum_{i=0}^{7}\binom{7}{i} 1000^{i}=(1000+1)^{7}=1001^{7}=7^{7} \cdot 11^{7} \cdot 13^{7}$

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.