Let p 11213 It turns out that p is a prime You may use tha

: Let p = 11213. It turns out that p is a prime. You may use that fact in this question. Find all integers b with the property that ordp(b) = 2. Find all integers b with the property that ordp(b) = 3.

Solution

p =11213

ordp(b) = 2

b=(p^2)u

b=(11213^2)u

where u is an integer not divisible by p.

so u = I - {k*11213}

where k is any integer.

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p =11213

ordp(b) = 3

b=(p^3)u

b=(11213^3)u

where u is an integer not divisible by p.

so u = I - {k*11213}

where k is any integer.

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