Bashing Available Part 1

Algebra Level 5

Given that:-

a1+a2+a3+a4=1a_1+a_2+a_3+a_4=1

a12+a22+a32+a42=2a_1^2+a_2^2+a_3^2+a_4^2=2

a13+a23+a33+a43=3a_1^3+a_2^3+a_3^3+a_4^3=3

a14+a24+a34+a44=4a_1^4+a_2^4+a_3^4+a_4^4=4;

The value of a15+a25+a35+a45a_1^5+a_2^5+a_3^5+a_4^5 can be expressed as the rational number pq\frac{p}{q}, where pp and qq are mutually prime positive integers. Determine p+qp+q.

amna_{m}^{n} is the nthn^{th} power of the number ama_m

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