So the prime divisors of 1000 are 2 and 5.
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- We are given that $ a + b = 1000 $, and $ p \mid a $, $ p \mid b $, so $ p \mid (a + b) = 1000 $. Therefore, $ p $ must be a prime divisor of 1000.
- Factor 1000:
- = 2^3 \cdot 5^3
- The largest possible prime
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