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Hari Shankar (9109)

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relatively prime means that they do not have any prime factors in common.

 

Any two consecutive numbers are relatively prime:

 

Proof: Let the numbers be n and n+1. If p is a prime that divides n and n+1, it also divides their difference =1

 

Likewise any two consecutive odd numbers are relatively prime, as proceeding as above p would have to divide 2 i.e. p =2, but we know that no odd number is divisible by 2.

 

So, 2n-1,2n, 2n+1 are all mutually relatively prime


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