﻿ A particular integer N is divisible by two different prime numbers p and q. Which

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 4 months ago

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 4 months ago

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