mersenneforum.org A great universal divisibility rule
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 2018-02-26, 19:06 #1 JM Montolio A   Feb 2018 10111112 Posts A great universal divisibility rule for n= 76657. Divider, Base, Pot, product 7, 10, 3, (7,6,6,5,7)*(81,27,9,3,1)= 7*115 47, 100, 6, (7,66,57)*(36,6,1)= 47*15 233, 1000, 68, (76,657)*(68,1)= 76*68+657*1= 233*25 Note Pot = Base mod Divider. Product is: the number on Base, MULTIPLIED BY, the powers of Pot. The rule is: (Divider | N) sii (Divider | Product) This rule is new. I think. JM M
2018-02-26, 22:13   #2
Nick

Dec 2012
The Netherlands

2·3·5·61 Posts

Quote:
 Originally Posted by JM Montolio A This rule is new. I think.JM M
It follows directly from the Binomial Theorem.

 2018-02-27, 11:52 #3 JM Montolio A   Feb 2018 10111112 Posts Not. Is new.
 2018-02-27, 16:11 #4 JM Montolio A   Feb 2018 5×19 Posts look some results: NBP e divisor de Me --------------------------------------- e 11000113 div 66000679 e 11000113 div 1232012657 e 11000189 div 3762064639 e 11000293 div 1386036919 e 11000299 div 374010167 e 11000369 div 88002953 e 11000387 div 1606056503 e 11000401 div 66002407 e 11000401 div 176006417 e 11000603 div 22001207 e 11000651 div 22001303 ----------------------------------------------------

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