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Difference between revisions of "2021 USAJMO Problems/Problem 1"

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==Problem==
 
==Problem==
  
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Find all primes, with proof, that are the average of 2 consecutive primes.
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==Solution==
 
==Solution==
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After 2, all primes are odd, and the average of 2 and 3 is not an integer.
 
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We proceed with mod 4. The 2 primes must be equivalent mod 4 because their difference cannot be 2 or 6 because that does not work.
 

Revision as of 18:46, 14 April 2021

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