SOLUTION: How do I prove that a prime number cannot be a sum of two or more consecutive positive odd integers?
This is my 7th grade extra credit. I wrote a list of primes. I have added
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-> SOLUTION: How do I prove that a prime number cannot be a sum of two or more consecutive positive odd integers?
This is my 7th grade extra credit. I wrote a list of primes. I have added
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Question 682679: How do I prove that a prime number cannot be a sum of two or more consecutive positive odd integers?
This is my 7th grade extra credit. I wrote a list of primes. I have added consecutive odd integers randomly. I know a prime cannot be the sum. I think there is a formula. x+[x+2]?? something with the powers of 2?
Please help
Ty
Let represent any positive odd integer. Then is the next consecutive positive odd integer.
The sum of these two positive odd integers is
Assume that is prime. But is divisible by 2 and therefore even. The only even prime number is 2, hence:
Which means that . But is neither positive nor odd, contradicting the original assumption about the nature of . Therefore, reductio ad absurdum, cannot be prime for any positive odd value of . Q.E.D.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
