Hey, I was just wondering gif someone could help me prove the following. ((p-1)/2)!)^ 2=(+ or -) 1 mod (p), where p is prime. THanks
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Originally Posted by HelloWorld2 Hey, I was just wondering gif someone could help me prove the following. ((p-1)/2)!)^ 2=(+ or -) 1 mod (p), where p is prime. THanks For p an odd prime, we have: (why?), so... Tonio Pd. If you in fact understand the above, then you must be able even to tell when exactly we'll get 1 and when -1 modulo p.
well, we'll get 1 when p=1mod(4), and -1 when p=-1mod(4). I realy don't get how you got that equaility.
Originally Posted by HelloWorld2 well, we'll get 1 when p=1mod(4), and -1 when p=-1mod(4). I realy don't get how you got that equaility. What're the inverses modulo p of ? Well, there you go. Tonio
Originally Posted by tonio What're the inverses modulo p of ? Well, there you go. Tonio But, for example, , and (If I understand what you meant.). The observation here is that for , we have . Then noting that shows that .
Originally Posted by melese But, for example, , and (If I understand what you meant.). I don't think you do, but for sure I don't understand you: "inverse" means "additive inverse", not "multiplicative inverse", as I think it was clear from the context of my answer, so your example is irrelevant, I believe, and what is relevant is what you wrote after that, which is what I was trying the OP to realize by himself. Tonio The observation here is that for , we have . Then noting that shows that . .
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