Shell Script to find Square-Triagular Numbers

Given this puzzle from Matt Parker, I wrote a swift little shell script to find the solution.

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for i in {1..100}; do
    I=$[i*i]
    for j in {1..100}; do
        J=$[(j*(j-1))/2]
        if [[ $I == $J ]]; then
            echo $I
        fi
    done
done

Not the most efficient solution, but still a fun exercise.