2021 AIME I #10
Consider the sequence $(a_k)_{k\\ge 1}$ of positive rational numbers defined by $a_1 = \\frac{2020}{2021}$ and for $k\\ge 1$, if $a_k = \\frac{m}{n}$ for relatively prime positive integers $m$ and $n$, then
\\a_{k+1} = \\frac{m + 18}{n+19}.\\Determine the sum of all positive integers $j$ such that the rational number $a_j$ can be written in the form $\\frac{t}{t+1}$ for some positive integer $t$.
\\a_{k+1} = \\frac{m + 18}{n+19}.\\Determine the sum of all positive integers $j$ such that the rational number $a_j$ can be written in the form $\\frac{t}{t+1}$ for some positive integer $t$.
2021 aime i #10fjioowefioweijiowejiowefjiopfopefiiowfwefpoeffewop