Multiple Choice Question (MCQ)

A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true?

I. N is not a prime number.

II. N is divisible by pq.

III. N is an odd integer.

  1. ×

    I only

  2. ×

    II only

  3. I and II only

  4. ×

    I and III only

  5. ×

    I, II, and III

Collected in the board: Number Theory

Steven Zheng posted 8 hours ago

Answer

  1. I, II, and III

    same as explanation in D. N must not be odd numbers.

    III is not true

  2. First, recall that a prime number is only divisible by itself and 1, and that 1 is not a prime number. So, statement I must be true, since a number that can be divided by different prime numbers p and q can’t be prime.

    Therefore I is true.


  3. Every number can be written as a product of a particular bunch of prime numbers. For this statement.

    N = \dots \cdot p\cdot q = \dots (pq)

    Therefore

    N must be divisible by pg

    II statement is true

  4. Based on the exaplnation above, I and II only

  5. I and III only

    Recall 6 can be divisible by prime two numbers 2 and 3. So N must not be odd numbers.

    III is not true

Steven Zheng posted 8 hours ago

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