Competition problem — Number theory

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Number theory Difficulty 4.6 AIME Find the answer

Compute the prime factorization of 1007021035035021007001.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

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

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Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.