Sam has a sequence of n consecutive positive integers a1,a2,a3⋯an where n is an odd number and a1 is an odd number. Adi arranges all of Sam's numbers in some permutation. Prove that given any permutation of the sequence (p1,p2,p3⋯pn). The expression:
⎝⎛k=1∏2n−1(p2k+6k)⎠⎞⎝⎛k=1∏2n+1(p2k−1+17k)⎠⎞
will always be divisible by 2.
Details and Assumptions
Basically, in the expression pa is added to 62a if a is even and 172a+1 if a is odd. Then all the brackets are multiplied together.
#Combinatorics
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