Given two integers n (n>1) and an odd prime p. Without loss of generality let p=2k1.
Prove that if C(n,2)  C(k,2) is divisible by p, it must be divisible also by p^{2}.
I guessed that p needed to be odd but not prime for this to work. I was able to prove that thought wrong:
n=8, k=5, p=9 (not prime)
C(8,2)C(5,2)=18 which is divisible by 9 but not 9^2
(It is divisible by 3 and 3^2 so the given problem may have a more general proof.)

Posted by Jer
on 20170108 16:13:31 