binomial coefficient modulo a prime


by erszega
Tags: binomial, coefficient, modulo, prime
erszega
erszega is offline
#1
Jun11-06, 02:37 AM
P: 36
A question:

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 ?
Phys.Org News Partner Science news on Phys.org
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
matt grime
matt grime is offline
#2
Jun11-06, 04:22 AM
Sci Advisor
HW Helper
P: 9,398
Yes, it's fermat's little theorem: x^p=x mod p, for p a prime, hence

(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.


Register to reply

Related Discussions
binomial coefficient Precalculus Mathematics Homework 5
[SOLVED] Binomial Coefficient Calculus & Beyond Homework 2
binomial coefficient modulo 2^n Linear & Abstract Algebra 19
Solving polynomial congruences modulo a prime power Calculus & Beyond Homework 0
Binomial Coefficient problem Introductory Physics Homework 2