Question

Prove that two consecutive positive integers are always coprime.​

Answer 1

Explanation:

There is no number which divides 1 except 1. So p=1 or you can say gcd(n,n+1)=p=1. Which implies n and n+1 are coprime.

Answer 2

Answer:

❀ʀᴇǫᴜɪʀᴇᴅ ᴀɴsᴡᴇʀ:

Let the numbers be I, I + 1:

They are co-prime if only +ve integer that divides both is 1.

I is given to be +ve integer.

So I = 1, 2, 3, ….

∴ One is odd and the other one is even. Hence H.C.F. of the two consecutive numbers is 1. Hence the result.

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