No. of ordered pairs in Combnations

(A)We try to check for all solutions other than (2013,1)& (2013,2012)

2013 = 3*11*61

Therefore n≥61.(otherwise it can never have the prime factor 61)

We can check that r =0,(61-0),1,(61-1),2,(61-2) does not satisfy the given condition.

For 58≥r≥3.

\inline \dpi{200} \binom{n}{r}\geq \binom{n}{3}\geq \binom{61}{3}> 2013

Hence no other solution can exist.

(B)Similarly for 2014 solutions other than (2014,1)& (2014,2013) does not exist.

a little hint can be drawn from the fact that all of non-proper divisors of 2013 are prime(3,11,61).