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2022 SSMO Team Round Problems/Problem 4

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Problem

Let $a_1=2,b_0=3, a_n=\left(a_{n-1}\right)^2,$ and $b_n=\left(b_{n-1}\right)^3.$ If $c_n=a_n+b_n,$ find the last two digits of $c_1+c_2+\dots+c_{2022}.$

Solution

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