- #1

- 36

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Let bin(a,b) denote the binomial coefficient a! / ( b! (a - b)! ).

Is it true that

bin( 2p, p ) = 2 (mod p) if p is prime and p>=3 ?

- Thread starter erszega
- Start date

- #1

- 36

- 0

Let bin(a,b) denote the binomial coefficient a! / ( b! (a - b)! ).

Is it true that

bin( 2p, p ) = 2 (mod p) if p is prime and p>=3 ?

- #2

matt grime

Science Advisor

Homework Helper

- 9,395

- 3

(1+x)^2p = (1+x^p)^2 = 1+2x^p+x^{2p} mod p

note your requirement on p>=3 is not necessary. 4 choose 2 =6 whcih is congruent to 2 mod 2 as well.

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