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Algebra Level 3

a1a2+a2a3+a3a4++an1an+ana1\large \frac{a_{1}}{a_{2}} + \frac{a_{2}}{a_{3}} + \frac{a_{3}}{a_{4}}+ \ldots+ \frac{a_{n-1}}{a_{n}} + \frac{a_{n}}{a_{1}}

Given a1,a2,a3,,an>0a_{1} , a_{2} , a_{3} ,\ldots , a_{n} > 0 for n>2n > 2. If the expression above has a minimum value of pnpn for pp is a positive integer, then find the value of p+1p + 1.

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