Problem 10 · 2018 Math Kangaroo
Medium
Number Theory
primesdivisibility
How many ways are there to write the number 1001 as the sum of two prime numbers?
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Answer: A — no way
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Hint 1 of 2
1001 is odd, so what must one of the two primes be?
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Hint 2 of 2
Test whether the forced partner is prime.
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Approach: parity forces one prime to be 2
- A sum of two primes that is odd must use 2 (the only even prime).
- Then the other prime would be 1001−2 = 999 = 3·333, which is not prime.
- So 1001 cannot be written as a sum of two primes — no way.
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