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$begingroup$

Hull-Dobell theorem says for $x_n+1= ax_n+c , mod, m$ if c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if

1. c and m are relatively prime




2. if q is prime and q | p then q | a-1




3. if 4 | m then 4 | a-1

if m is prime and a < p then the sequence must have the full period but take
a=4, c= 5, p=11 and $x_0 = 0$. Then the sequence will
be 5,3,6,7,0,5,3,6,7,0,5. (the period is 5)
but we don't have the full period, why? what is missing here?.

recursive-algorithms

share|cite|improve this question

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

$endgroup$

add a comment | 

0

$begingroup$

Hull-Dobell theorem says for $x_n+1= ax_n+c , mod, m$ if c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if

1. c and m are relatively prime




2. if q is prime and q | p then q | a-1




3. if 4 | m then 4 | a-1

if m is prime and a < p then the sequence must have the full period but take
a=4, c= 5, p=11 and $x_0 = 0$. Then the sequence will
be 5,3,6,7,0,5,3,6,7,0,5. (the period is 5)
but we don't have the full period, why? what is missing here?.

recursive-algorithms

share|cite|improve this question

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

$endgroup$

add a comment | 

$begingroup$

Hull-Dobell theorem says for $x_n+1= ax_n+c , mod, m$ if c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if

1. c and m are relatively prime




2. if q is prime and q | p then q | a-1




3. if 4 | m then 4 | a-1

if m is prime and a < p then the sequence must have the full period but take
a=4, c= 5, p=11 and $x_0 = 0$. Then the sequence will
be 5,3,6,7,0,5,3,6,7,0,5. (the period is 5)
but we don't have the full period, why? what is missing here?.

recursive-algorithms

share|cite|improve this question

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

$endgroup$

share|cite|improve this question

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

share|cite|improve this question

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

edited Mar 29 at 22:14

Bernard

124k741116

edited Mar 29 at 22:14

Bernard

124k741116

asked Mar 29 at 21:18

Richard KimRichard Kim

11

asked Mar 29 at 21:18

Richard KimRichard Kim

11