At least one of 3 consecutive odd numbers is a multiple of 3

Posted on February 21, 2017 by Sumant Sumant

The first example is 3,5,7 all these are primes but beyond that if there are three consecutive odds one of them will always be a prime.
Let three consecutive odd numbers be 2n+1,2n+3,2n+5.
If 2n+1 is a multiple of 3 then we are done.
Else the remainder when divided by 3 is either 1 or 2. Suppose its 1 then it means 2x is divisible by 3 which means 2x+3 is divisible by 3.
Or suppose the remainder is 2, which means 2x-1 is divisible by 3 which means 2x+2 and 2x+5 are divisible by 3. Hence proved.

About Sumant Sumant

I love Math and I am always looking forward to collaborate with fellow learners. If you need help learning math then please do contact me.
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