Competition problem — Number theory

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Number theory Difficulty 4.7 AIME Find the answer

Given that 7,999,999,999 has at most two prime factors, find its largest prime factor.

Your answer

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

Solution

7,999,999,999=8 \cdot 10^{9}-1=2000^{3}-1=(2000-1)\left(2000^{2}+2000+1\right) $, so \left(2000^{2}+2000+1\right)=4,002,001$ is its largest prime factor.

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