Each of p and 8p -1 is a prime number.
Is 8p+1 a prime number?
- If so, provide an example.
- If not, prove it.
Computer program and spreadsheet aided methodologies are welcome, but an analytical solution is preferred.
*** Adapted from a problem appearing in a Russian Mathematical Olympiad.
If the prime is 3, 8*p-1 = 23, and *p+1 = 25 and is not prime.
For primes other than 3:
8p is not a multiple of 3.
8p-1 is stated to be prime and therefore not a multiple of 3.
8p+1 is the third of three integers in a row and the other two are not a multiple of 3, so it must be a multiple of 3 and not prime.
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Posted by Charlie
on 2022-11-27 09:49:40 |
solution
