Expand by the binomial expansion:



Every term in that summation except the very last one 
is a multiple of 68.  So we separate the summation into 
the summation of all the terms except the last one and 
then add the last term to that:



and since 


 

Every term in the summation is a multiple of 68, so the whole
summation is a multiple of 68, so let's label that summation as 
68n, for some positive integer n.

So we have



Therefore





So the remainder when divided by 68 will be 66

Answer: 66

Edwin