Topic content:
Let a be a prime number, and both 7a2+8 and 8a2+7 are prime numbers. If x=77a+8, y=88a+7, then in the following cases, it must be true that () A. x, y are all prime numbers B. x, y are all composite numbers C. x, y is a prime number, and a composite number D. For different a, the above situations may occur
Best answer:
▄ ① When a=3, 7a2+8=71 and 8a2+7=79 are prime numbers, while x=77a+8=239 and y=88a+7=271 are prime numbers;
② When the prime number a is different from 3, then a2 is divided by 3 and 1 is left. Let a2=3n+1, then 7a2+8=21n+15, 8a2+7=24n+15. They are not prime numbers and contradict the conditions.
So we can know from ① ② that x and y are prime numbers
Therefore, A
Answer analysis:
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Test core:
Definition of rational number: rational number is the general name of integer and fraction. All rational numbers can be transformed into fractions.