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 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.
