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Let pn denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If pn+1-pn=66, then the sum of all distinct prime divisors of n is :
(3) 5
No three vertices of a regular polygon are collinear, so pn=nC3.
pn+1-pn=n+1C3-nC3=nC2
n(n-1)2=66 n2-n-132=0
(n-12)(n+11)=0 n=12
12=22 3; distinct prime divisors: 2 and 3
Sum =2+3=5
Answer: (3)
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