Antisha
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 Jan 29 comment Prime numbers characterization Thank you Barry, I think that it is a good advice not to post here until I have enough experience, and I think I do not have so much experience as you people who post here, I will post on mathstackexchange and if I ever acquire enough knowledge I will probably come back here. Bye bye. :) Jan 29 comment Mersenne primes problem I didn´t see this at the time of writing my post, but I would like when it is posted now that you give an opinion about the result, if it is not good enough I will post no more here. Jan 29 asked Prime numbers characterization Jan 29 comment Mersenne primes problem I will now write a post about something about prime numbers that I managed to prove so I would like to see your comments about usefulness of such a formula. Jan 29 accepted Mersenne primes problem Jan 29 comment Mersenne primes problem I am amazed how two of you see these things in a so short period of time. Okay, I will post no more until I have a really good question that is on the research level. Thank you. Jan 29 asked Mersenne primes problem Jan 28 comment Numbers of a certain form not expressible as squares These are two problems, not a system of equations Jan 28 comment Numbers of a certain form not expressible as squares Is it possible to attack this with modular arithmetic? Solve in positive integers, with $n\geq9$ $81k^2+18k-n!=0$ and $81k^2-18k-n!=0$ Jan 28 awarded Commentator Jan 28 comment Numbers of a certain form not expressible as squares Oh well I did it in different way, look now when it is edited. Jan 28 awarded Editor Jan 28 revised Numbers of a certain form not expressible as squares added 1290 characters in body Jan 28 comment Numbers of a certain form not expressible as squares I found an elementary proof that $a^n + 1\neq m^2$ when $a$ is of the form $a=3k+4$. In it I used the properties of this function: mathworld.wolfram.com/DigitalRoot.html Thank you all for your valuable information. Jan 28 accepted Numbers of a certain form not expressible as squares Jan 28 comment Numbers of a certain form not expressible as squares No need for posting, the fact that I discovered is easily obtained. Jan 28 comment Numbers of a certain form not expressible as squares Close this one, I will post now another question and the fact that I discovered about it. Jan 28 comment Numbers of a certain form not expressible as squares Motivation is to find elementary proof when $a$ is of the form $a=3k+4$ when k is natural number, or zero. Jan 28 comment Numbers of a certain form not expressible as squares Thank you, I forgot that Catalan´s conjecture have status of a theorem, and sure there must be some elementary method for proving these three cases. Jan 28 asked Numbers of a certain form not expressible as squares