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

m
Line 2: Line 2:
  
 
Find all primes, with proof, that are the average of 2 consecutive primes.
 
Find all primes, with proof, that are the average of 2 consecutive primes.
 +
 +
==Solution==
 +
After 2, all primes are odd, and the average of 2 and 3 is not an integer.
 +
 +
We proceed with mod 4. The 2 primes must be equivalent mod 4.

Revision as of 19:14, 12 April 2021

Problem

Find all primes, with proof, that are the average of 2 consecutive primes.

Solution

After 2, all primes are odd, and the average of 2 and 3 is not an integer.

We proceed with mod 4. The 2 primes must be equivalent mod 4.

Invalid username
Login to AoPS