Question

9.41:01 Question 4 Give an example of four different integers a, b, c, d such that there exists no positive integer n for which a +b , c+n, and d + n are pairwise relatively prime,​

Answer 1

Given:

integers a, b, c, d

Let numbers could be a = 1, b = 2, c = 3 and d = 4

If n is odd

a + n and c + n will be even, hence not relatively prime.

If n is even

b + n and d + n will be even, hence not relatively prime.

Hence a +b , c +n, and d + n  pair is not relatively prime.

Answer 2

As we know that,

Given:

The integers  $a, b, c, d$

Find out :

Give an example of four different integers a, b, c, d.

Let us :

consider numbers could be $a = 1, b = 2, c = 3$and $d = 4$

If n is odd,

$a + n$ and $c + n$will be even, hence not relatively prime.

If n is even,

b + n and d + n will be even, hence not relatively prime.

So that$a +b, c +n,$ and $d + n$  pair are not relatively prime.