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There is a sequence of positive numbers $$a_1,a_2,a_3,...a_{m}$$ such that $$a_1=19,a_2=98,a_m=0,$$ and

$$a_{n+2}=a_n-\frac{2}{a_{n+1}},$$ for $$n=1,2,...,m-2$$.

Find the value of $$m$$.

Aug 5, 2022