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PFA

A bit tedious problem and that requires a lot of cases, but the answer is so surprising. The introductory part really helped to form the two assumptions, one that (k-1)(k)(k+1) is divisible by 3, and the other is of figuring out the range for 10k-k^2. Knowing (k-1)(k)(k+1) is divisible by 3, helped in other problems as well

Unrelated, but, happy π day!! Here is one problem's solution that I made on my YouTube channel (MathyMahdi) that involves invariant areas and the answer comes out to be pi: https://www.youtube.com/watch?v=ub2AvnCtNuE&t=6s