Difference between revisions of "2016 AMC 12A Problems/Problem 5"
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==Solution== | ==Solution== | ||
| + | In this case, a counterexample is a number that would prove Goldbach's conjecture false. The conjecture asserts what '''can''' be done with '''even''' integers greater than 2. | ||
| + | Therefore the solution is <cmath>{\textbf{(E)}\text{ an even integer greater than 2 that cannot be written as the sum of two prime numbers.}}</cmath> | ||
==See Also== | ==See Also== | ||
| − | {{AMC12 box|year=2016|ab=A|num-b= | + | {{AMC12 box|year=2016|ab=A|num-b=4|num-a=6}} |
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 11:40, 5 February 2016
Problem
Goldbach's conjecture states that every even integer greater than 2 can be written as the sum of two prime numbers (for example, 
). So far, no one has been able to prove that the conjecture is true, and no one has found a counterexample to show that the conjecture is false. What would a counterexample consist of?
Solution
In this case, a counterexample is a number that would prove Goldbach's conjecture false. The conjecture asserts what can be done with even integers greater than 2.
Therefore the solution is ![\[{\textbf{(E)}\text{ an even integer greater than 2 that cannot be written as the sum of two prime numbers.}}\]](http://latex.artofproblemsolving.com/d/0/1/d01c4e58ff9cbe484d3837f31384574d5e6fa60f.png)
See Also
| 2016 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 4 |
Followed by Problem 6 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
