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Let n and k be positive integers such that \(n < 10^6\) and

\(32 \binom{6}{6} + 31 \binom{7}{6} + 30 \binom{8}{6} + \dots + 3 \binom{35}{6} + 2 \binom{36}{6} + \binom{37}{6} = \binom{n}{k}.\)
Enter the ordered pair (n,k)

 Dec 30, 2019
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 n=32; k=6; p=0;a= n*k nCr 6;p=p+a;n--;k++;if(k<=37, goto3,0);printp;a=10; b=1;c= a nCr b; if(c==61523748, goto4, goto5);printc, a, b; a++;if(a<100, goto2, 0);a=10;b++;if(b<100, goto2, discard=0;

 

Sum =61,523, 748 

n = 39   and   k = 8, and 

n = 39   and   k =31

 Dec 30, 2019

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