BZP says "Chinese Remainder Theorem"

[NotLKH]

FYI:

Given the numbers 0 thru n, if you use the First R Prime numbers, and mod them, Just so long as N < the Multple of the first R prime numbers, then you will end up with a unique numerical sequence that represents each such number.

ie..: Referencing the primes 2,3,and 5, the numbers 0 thru 7 could be seen as:


0=0,0,0
1=1,1,1
2=0,2,2
3=1,0,3
4=0,1,4
5=1,2,0
6=0,0,1
7=1,1,2

and so on...

Obviuosly Cols 1, 2, and 3 are the results of taking the Target number and Modding it by the prime whose index is identical to that of the columns.


But, heres the delema: How do you go in revers?


Well, if you only use the primes 2 and 3, the equation is:

Num = {3*Pos(Prime2) + 4*Pos(Prime3)} Mod 2*3

If you use 2,3, and 5:

Num = {15*Pos(Prime2) + 10*Pos(Prime3) + 6*Pos(Prime5)} Mod 2*3*5

and actually, its really simple to figure, once youve done your homework.

Check the attached table:

to be continued...





errr? Wheres the image???