# Bashing Available Part 1

Algebra Level 5

Given that:-

$$a_1+a_2+a_3+a_4=1$$

$$a_1^2+a_2^2+a_3^2+a_4^2=2$$

$$a_1^3+a_2^3+a_3^3+a_4^3=3$$

$$a_1^4+a_2^4+a_3^4+a_4^4=4$$;

The value of $$a_1^5+a_2^5+a_3^5+a_4^5$$ can be expressed as the rational number $$\frac{p}{q}$$, where $$p$$ and $$q$$ are mutually prime positive integers. Determine $$p+q$$.

$$a_{m}^{n}$$ is the $$n^{th}$$ power of the number $$a_m$$

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