compute a pseudo primitive root - Maple Help

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numtheory[pprimroot] - compute a pseudo primitive root

Calling Sequence

pprimroot(g, n)

pprimroot(n)

Parameters

g

-

positive integer or 0

n

-

integer greater than 1

Description

• 

The function pprimroot(g, n) computes the next primitive root larger than g or, if n does not have primitive roots, computes a number which is not a root of order of any of the factors of φn.

• 

Thus (in all cases), find an integer y, such that there is no x for which xr=ymodn when r is a divisor of φn greater than 1 and igcdy,n=1.

• 

If only one argument n is present then this function will return the smallest primitive root of the number n. If there is no primitive root of n then this function will return the smallest integer y, such that there is no x for which xr=ymodn when r is a divisor of φn greater than 1 and igcdy,n=1.

• 

The command with(numtheory,pprimroot) allows the use of the abbreviated form of this command.

Examples

withnumtheory:

pprimroot1,41

6

(1)

pprimroot2,8

3

(2)

pprimroot24

5

(3)

See Also

numtheory[order], numtheory[primroot]


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