By Doron Zeilberger

.pdf .ps .tex

Written: March 22, 2009.

[Appeared in J. of Difference Equations and Applications, v. 17, No. 3, (March 2011) , 375-386]

Paul Erdos claimed that mathematics is not yet ready to settle the 3x+1 conjecture. I agree, but very soon it will be! With the exponential growth of computer-generated mathematics, we (or rather our silicon brethrern) would have a shot at it. Of course, not by

Added May 11, 2010: Watch the movie (produced by Edinah Gnang)

- LADAS, a Maple package that does all the phases of mathematical research, conjecturing, suggesting proofs, and formally proving.
- COLLATZ, a Maple package that (empirically) investigates one-dimensional generalizations of the 3x+1 conjecture, where instead of mod 2, you can have mod m. It is "just" for empirical investigation, and so far has no proving capabilities.

maple -q < inSefer > oSefer

you would get, after 1444 seconds of CPU time, the following marvelous 144 theorems and lemmas (complete with proofs!).

- Theorem 1 that uses the inequality scheme in Lemma 1.
- Theorem 2 that uses the inequality scheme in Lemma 2.
- Theorem 3 that uses the inequality scheme in Lemma 3.
- Theorem 4 that uses the inequality scheme in Lemma 4.
- Theorem 5 that uses the inequality scheme in Lemma 5.
- Theorem 6 that uses the inequality scheme in Lemma 6.
- Theorem 7 that uses the inequality scheme in Lemma 7.
- Theorem 8 that uses the inequality scheme in Lemma 8.
- Theorem 9 that uses the inequality scheme in Lemma 9.
- Theorem 10 that uses the inequality scheme in Lemma 10.
- Theorem 11 that uses the inequality scheme in Lemma 11.
- Theorem 12 that uses the inequality scheme in Lemma 12.
- Theorem 13 that uses the inequality scheme in Lemma 13.
- Theorem 14 that uses the inequality scheme in Lemma 14.
- Theorem 15 that uses the inequality scheme in Lemma 15.
- Theorem 16 that uses the inequality scheme in Lemma 16.
- Theorem 17 that uses the inequality scheme in Lemma 17.
- Theorem 18 that uses the inequality scheme in Lemma 18.
- Theorem 19 that uses the inequality scheme in Lemma 19.
- Theorem 20 that uses the inequality scheme in Lemma 20.
- Theorem 21 that uses the inequality scheme in Lemma 21.
- Theorem 22 that uses the inequality scheme in Lemma 22.
- Theorem 23 that uses the inequality scheme in Lemma 23.
- Theorem 24 that uses the inequality scheme in Lemma 24.
- Theorem 25 that uses the inequality scheme in Lemma 25.
- Theorem 26 that uses the inequality scheme in Lemma 26.
- Theorem 27 that uses the inequality scheme in Lemma 27.
- Theorem 28 that uses the inequality scheme in Lemma 28.
- Theorem 29 that uses the inequality scheme in Lemma 29.
- Theorem 30 that uses the inequality scheme in Lemma 30.
- Theorem 31 that uses the inequality scheme in Lemma 31.
- Theorem 32 that uses the inequality scheme in Lemma 32.
- Theorem 33 that uses the inequality scheme in Lemma 33.
- Theorem 34 that uses the inequality scheme in Lemma 34.
- Theorem 35 that uses the inequality scheme in Lemma 35.
- Theorem 36 that uses the inequality scheme in Lemma 36.
- Theorem 37 that uses the inequality scheme in Lemma 37.
- Theorem 38 that uses the inequality scheme in Lemma 38.
- Theorem 39 that uses the inequality scheme in Lemma 39.
- Theorem 40 that uses the inequality scheme in Lemma 40.
- Theorem 41 that uses the inequality scheme in Lemma 41.
- Theorem 42 that uses the inequality scheme in Lemma 42.
- Theorem 43 that uses the inequality scheme in Lemma 43.
- Theorem 44 that uses the inequality scheme in Lemma 44.
- Theorem 45 that uses the inequality scheme in Lemma 45.
- Theorem 46 that uses the inequality scheme in Lemma 46.
- Theorem 47 that uses the inequality scheme in Lemma 47.
- Theorem 48 that uses the inequality scheme in Lemma 48.
- Theorem 49 that uses the inequality scheme in Lemma 49.
- Theorem 50 that uses the inequality scheme in Lemma 50.
- Theorem 51 that uses the inequality scheme in Lemma 51.
- Theorem 52 that uses the inequality scheme in Lemma 52.
- Theorem 53 that uses the inequality scheme in Lemma 53.
- Theorem 54 that uses the inequality scheme in Lemma 54.
- Theorem 55 that uses the inequality scheme in Lemma 55.
- Theorem 56 that uses the inequality scheme in Lemma 56.
- Theorem 57 that uses the inequality scheme in Lemma 57.
- Theorem 58 that uses the inequality scheme in Lemma 58.
- Theorem 59 that uses the inequality scheme in Lemma 59.
- Theorem 60 that uses the inequality scheme in Lemma 60.
- Theorem 61 that uses the inequality scheme in Lemma 61.
- Theorem 62 that uses the inequality scheme in Lemma 62.
- Theorem 63 that uses the inequality scheme in Lemma 63.
- Theorem 64 that uses the inequality scheme in Lemma 64.
- Theorem 65 that uses the inequality scheme in Lemma 65.
- Theorem 66 that uses the inequality scheme in Lemma 66.
- Theorem 67 that uses the inequality scheme in Lemma 67.
- Theorem 68 that uses the inequality scheme in Lemma 68.
- Theorem 69 that uses the inequality scheme in Lemma 69.
- Theorem 70 that uses the inequality scheme in Lemma 70.
- Theorem 71 that uses the inequality scheme in Lemma 71.
- Theorem 72 that uses the inequality scheme in Lemma 72.
- Theorem 73 that uses the inequality scheme in Lemma 73.
- Theorem 74 that uses the inequality scheme in Lemma 74.
- Theorem 75 that uses the inequality scheme in Lemma 75.
- Theorem 76 that uses the inequality scheme in Lemma 76.
- Theorem 77 that uses the inequality scheme in Lemma 77.
- Theorem 78 that uses the inequality scheme in Lemma 78.
- Theorem 79 that uses the inequality scheme in Lemma 79.
- Theorem 80 that uses the inequality scheme in Lemma 80.
- Theorem 81 that uses the inequality scheme in Lemma 81.
- Theorem 82 that uses the inequality scheme in Lemma 82.
- Theorem 83 that uses the inequality scheme in Lemma 83.
- Theorem 84 that uses the inequality scheme in Lemma 84.
- Theorem 85 that uses the inequality scheme in Lemma 85.
- Theorem 86 that uses the inequality scheme in Lemma 86.
- Theorem 87 that uses the inequality scheme in Lemma 87.
- Theorem 88 that uses the inequality scheme in Lemma 88.
- Theorem 89 that uses the inequality scheme in Lemma 89.
- Theorem 90 that uses the inequality scheme in Lemma 90.
- Theorem 91 that uses the inequality scheme in Lemma 91.
- Theorem 92 that uses the inequality scheme in Lemma 92.
- Theorem 93 that uses the inequality scheme in Lemma 93.
- Theorem 94 that uses the inequality scheme in Lemma 94.
- Theorem 95 that uses the inequality scheme in Lemma 95.
- Theorem 96 that uses the inequality scheme in Lemma 96.
- Theorem 97 that uses the inequality scheme in Lemma 97.
- Theorem 98 that uses the inequality scheme in Lemma 98.
- Theorem 99 that uses the inequality scheme in Lemma 99.
- Theorem 100 that uses the inequality scheme in Lemma 100.
- Theorem 101 that uses the inequality scheme in Lemma 101.
- Theorem 102 that uses the inequality scheme in Lemma 102.
- Theorem 103 that uses the inequality scheme in Lemma 103.
- Theorem 104 that uses the inequality scheme in Lemma 104.
- Theorem 105 that uses the inequality scheme in Lemma 105.
- Theorem 106 that uses the inequality scheme in Lemma 106.
- Theorem 107 that uses the inequality scheme in Lemma 107.
- Theorem 108 that uses the inequality scheme in Lemma 108.
- Theorem 109 that uses the inequality scheme in Lemma 109.
- Theorem 110 that uses the inequality scheme in Lemma 110.
- Theorem 111 that uses the inequality scheme in Lemma 111.
- Theorem 112 that uses the inequality scheme in Lemma 112.
- Theorem 113 that uses the inequality scheme in Lemma 113.
- Theorem 114 that uses the inequality scheme in Lemma 114.
- Theorem 115 that uses the inequality scheme in Lemma 115.
- Theorem 116 that uses the inequality scheme in Lemma 116.
- Theorem 117 that uses the inequality scheme in Lemma 117.
- Theorem 118 that uses the inequality scheme in Lemma 118.
- Theorem 119 that uses the inequality scheme in Lemma 119.
- Theorem 120 that uses the inequality scheme in Lemma 120.
- Theorem 121 that uses the inequality scheme in Lemma 121.
- Theorem 122 that uses the inequality scheme in Lemma 122.
- Theorem 123 that uses the inequality scheme in Lemma 123.
- Theorem 124 that uses the inequality scheme in Lemma 124.
- Theorem 125 that uses the inequality scheme in Lemma 125.
- Theorem 126 that uses the inequality scheme in Lemma 126.
- Theorem 127 that uses the inequality scheme in Lemma 127.
- Theorem 128 that uses the inequality scheme in Lemma 128.
- Theorem 129 that uses the inequality scheme in Lemma 129.
- Theorem 130 that uses the inequality scheme in Lemma 130.
- Theorem 131 that uses the inequality scheme in Lemma 131.
- Theorem 132 that uses the inequality scheme in Lemma 132.
- Theorem 133 that uses the inequality scheme in Lemma 133.
- Theorem 134 that uses the inequality scheme in Lemma 134.
- Theorem 135 that uses the inequality scheme in Lemma 135.
- Theorem 136 that uses the inequality scheme in Lemma 136.
- Theorem 137 that uses the inequality scheme in Lemma 137.
- Theorem 138 that uses the inequality scheme in Lemma 138.
- Theorem 139 that uses the inequality scheme in Lemma 139.
- Theorem 140 that uses the inequality scheme in Lemma 140.
- Theorem 141 that uses the inequality scheme in Lemma 141.
- Theorem 142 that uses the inequality scheme in Lemma 142.
- Theorem 143 that uses the inequality scheme in Lemma 143.
- Theorem 144 that uses the inequality scheme in Lemma 144.

Doron Zeilberger's List of Papers