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  3. A student made a conjecture that for any integer n, the integer An + 3 is a prim

A student made a conjecture that for any integer n, the integer An + 3 is a prim

游客2025-02-24  29
问题 A student made a conjecture that for any integer n, the integer An + 3 is a prime number. Which of the following values of n could be used to disprove the student’s conjecture?
Indicate all such values.
选项 A、1
B、3
C、4
D、6
E、7
答案 B，D
解析 Recall that a prime number is an integer greater than 1 that has no positive divisors other than 1 and itself.
    The answer choices for this question are integer values of n. Any of the answer choices for which the integer 4n + 3 is not a prime number could be used to disprove the conjecture that for any integer n, the integer An + 3 is a prime number.
    To answer this question, you must determine for each of the answer choices whether the integer 4n + 3 is a prime number. The evaluations are as follows:
Choice A: For n=1, the integer 4n + 3 is 4(1)+ 3, or 7, which is a prime number.
Choice B: For n = 3, the integer 4n + 3 is 4(3)+ 3, or 15, which is not a prime number.
Choice C: For n = 4, the integer An + 3 is 4(4)+ 3, or 19, which is a prime number.
Choice D: For n = 6, the integer An + 3 is 4(6)+ 3, or 27, which is not a prime number.
Choice E: For n = 7, the integer 4n + 3 is 4(7)+ 3, or 31, which is a prime number.
Therefore, of the answer choices, only Choices B and D, that is, n = 3 and n = 6, result in integers 4n + 3 that are not prime numbers. Thus, the correct answer consists of Choices B and D.
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