Ju n 20 08 Examples of finite p - divisible sets of MHS
نویسنده
چکیده
Hence J2(2|7) = ∅ and consequently J(2|7) = {0, 3, 6, 26}. For all the other primes p 6= 7 from 5 up to 1061 we find that J1(2|p) = {0, (p− 1)/2, p− 1} ∪ T (2|p) ∪ {p− 1− r : r ∈ T (2|p)} where T (2|p) are listed in Table 1 if T (2|p) 6= ∅. Moreover, J1(2|p) = ∅ which implies J(2|p) = {(p− 1)/2, p− 1} ∪ T (2|p) ∪ {p− 1− r : r ∈ T (2|p)} in this range. p T (2|p) p T (2|p) p T (2|p) p T (2|p) p T (2|p) p T (2|p) 37 15 163 61 419 111 563 175,227 677 153 883 151 41 4 167 61 421 59 569 199 709 123 911 345 43 11 181 85 433 179 571 247 727 197,239 929 64 59 6,24 211 99 457 216 577 134,158 739 93 953 199 97 15 241 60,96 467 158,170 601 17 787 344 967 463 107 39 269 50 479 5 617 97 797 185,226 971 429 127 23 307 27 487 32 619 16,70,286 811 371 991 72 137 44 311 43 491 173 643 17,222 821 39 997 205,310 149 37 373 54 499 134 653 246,307 859 414 1013 430 157 25 383 150 547 165 659 232 863 226 1031 384
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The following examples give evidence to the following conjecture contained in my paper [2]. All the main theoretical results can be found in that paper. Conjecture 1. Let d be a positive integer and ~s ∈ N. Then the set J(~s|p) is finite for every prime p. Example 2. The first example we would like to do is about the partial sums of ζ(2) series. The prime p = 7 is a little different from the ot...
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