Consequences of Getting More Than a Half
If more than half of the integers from
 |Contact| |Front page| |Contents| |Up| |Store| Copyright © 1996-2012 Alexander Bogomolny
If more than half of the integers from
Form pairs of consecutive integers:
There are n such pairs. By the Pigeonhole Principle, there is at least one pair with two selected integers. But these then differ by 1 and, hence, are mutually prime. (This proof has been found by Paul Erdös' protege, Louis P´sa when he was 12 years old. See [Honsberger, pp. 10-21].) Reference
|Contact| |Front page| |Contents| |Up| |Store| Copyright © 1996-2012 Alexander Bogomolny |
| 41170202 |
