1983 AMC 12 第 3 题

Question

三个素数

p

、

q

、

r

满足

p+q=r

和

1\lt p\lt q

。则

p

等于

Three primes,

p,

q

and

r,

satisfy

p+q=r

and

1\lt p\lt q.

Then

p

equals

2

3

7

13

17

除一个素数外，其余素数都是奇数

Every prime except one is odd

若两个加数都是奇数，它们的和就是一个大于

2

的偶数

If both addends were odd, their sum would be an even number greater than

2

若

p

和

q

都是奇数，则

r=p+q

是大于

2

的偶数，因而不是素数。所以其中一个加数是唯一的偶素数

2

。由于

p\lt q

，这个加数就是

p

。

所以正确答案是 A。

If both

p

and

q

were odd, then

r=p+q

would be even and greater than

2,

so it would not be prime. Thus one addend is the only even prime,

2.

Since

p\lt q,

that addend is

p.

Therefore, the correct answer is A.

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