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-   -   How do we calculate the weight? (https://www.mersenneforum.org/showthread.php?t=25232)

sweety439 2020-02-14 12:30

How do we calculate the weight?
 
How do we calculate [B]the weight[/B] for a form (k*b^n+c)/gcd(k+c,b-1) for fixed integers k >= 1, b >= 2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1.

I have a [URL="https://mersenneforum.org/showpost.php?p=529838&postcount=675"]research[/URL] that whether the form (k*b^n+c)/gcd(k+c,b-1) can contain a prime (there are special cases, such as (27*8^n+1)/7, (1*8^n-1)/7, (1*16^n-1)/15, and (4*16^n+1)/5, they can contain [I][B]only one[/B][/I] prime (because of the algebra factors), thus the weight is also 0, besides, there are also cases without covering set or algebra factors, but cannot contain a prime, such as 8*128^n+1 and 32*128^n+1)

(I know that the [URL="https://mersenneforum.org/showthread.php?t=21954"]dual forms[/URL] have the same weight)


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