# Question: Suppose a pseudorandom sequence is constructed using the power residue

Suppose a pseudorandom sequence is constructed using the power residue method. If q = 11, find a value of that leads to a sequence with maximum possible period.

X k = ax k – 1 mod q, k = 1, 2, 3…

Find the period and the sequence which results for the following values of (a, q). For each case, assume the seed is xo = 1.

(a) a = 4, q = 9,

(b) a = 5, q = 9,

(c) a = 2, q = 5,

(d) a = 5, q = 11,

X k = ax k – 1 mod q, k = 1, 2, 3…

Find the period and the sequence which results for the following values of (a, q). For each case, assume the seed is xo = 1.

(a) a = 4, q = 9,

(b) a = 5, q = 9,

(c) a = 2, q = 5,

(d) a = 5, q = 11,

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