AMC12 2016 A

AMC12 2016 A · Q5

AMC12 2016 A · Q5. It mainly tests Logic puzzles.

Goldbach’s conjecture states that every even integer greater than $2$ can be written as the sum of two prime numbers (for example, $2016 = 13 + 2003$). 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?

哥德巴赫猜想断言：每个大于 $2$ 的偶整数都可以写成两个素数之和（例如，$2016 = 13 + 2003$）。到目前为止，还没有人能够证明该猜想为真，也没有人找到反例来说明该猜想为假。一个反例应当由什么构成？

(A) an odd integer greater than 2 that can be written as the sum of two prime numbers 大于2的奇整数，可写成两个素数之和

(B) an odd integer greater than 2 that cannot be written as the sum of two prime numbers 大于2的奇整数，不可写成两个素数之和

(D) an even integer greater than 2 that can be written as the sum of two prime numbers 大于2的偶整数，可写成两个素数之和

(E) an even integer greater than 2 that cannot be written as the sum of two prime numbers 大于2的偶整数，不可写成两个素数之和

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): A counterexample must satisfy the hypothesis of being an even integer greater than 2 but fail to satisfy the conclusion that it can be written as the sum of two prime numbers.

答案（E）：反例必须满足“是一个大于 2 的偶整数”这一假设，但不满足“它可以写成两个素数之和”这一结论。

Topics

LM.001 Logic puzzles