• m_f@midwest.socialEnglish
    13·
    3 hours ago

    ⅐ = 0.1̅4̅2̅8̅5̅7̅

    The above is 42857 * 7, but you also get interesting numbers for other subsets:

         7 * 7 =     49
    57 * 7 =    399
   857 * 7 =   5999
  2857 * 7 =  19999
 42857 * 7 = 299999
142857 * 7 = 999999

    Related to cyclic numbers:

    142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
142857 * 7 = 999999
  • OfficerBribe@lemm.eeEnglish
    9·
    7 hours ago

    Never realized there are so many rules for divisibility. This post fits in this category:

    Forming an alternating sum of blocks of three from right to left gives a multiple of 7

    299,999 would be 999 - 299 = 700 which is divisible by 7. And if we simply swap grouped digits to 999,299, it is also divisible by 7 since 299 - 999 = -700.

    And as for 13:

    Form the alternating sum of blocks of three from right to left. The result must be divisible by 13

    So we have 999 - 999 + 299 = 299.

    You can continue with other rules so we can then take this

    Add 4 times the last digit to the rest. The result must be divisible by 13.

    So for 299 it’s 29 + 9 * 4 = 65 which divides by 13. Pretty cool.