a) Letpbe an odd prime and let

a = (2j-1) = (1)(3)(5)....(p-2)

Prove that = mod p

(Product is from j=1 to (p-1)/2)

b) Letpbe a prime. Prove that

= 2 mod p

is 2p choose p, as in statistics. so

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- Oct 18th 2010, 09:36 PMJanu42Congruence Problems
a) Let

*p*be an odd prime and let

a = (2j-1) = (1)(3)(5)....(*p*-2)

Prove that = mod p

(Product is from j=1 to (p-1)/2)

b) Let*p*be a prime. Prove that

= 2 mod p

is 2p choose p, as in statistics. so - Oct 18th 2010, 10:13 PMAlso sprach Zarathustra
Hint for a:

Wilson theorem. - Oct 18th 2010, 10:19 PMJanu42
- Oct 18th 2010, 10:30 PMAlso sprach Zarathustra
Another hint(or solution)...

, so

...