2021 USAJMO Problems/Problem 1: Difference between revisions
No edit summary |
mNo edit summary |
||
| 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 18:14, 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.
