 
Summary: CS681: Endterm Examination
Maximum Marks: 50
Due by Nov 18, 2009, 19:00 Hrs
Question 1 (marks 10). In the deterministic primality test discussed in
the class, one needed to test the equation
(X + a)n
= Xn
+ a (mod n, Xr
 1)
for every a 2
r log n. Suppose we know a number Zn such that
=
n1
r Zn is a primitive rth root of unity (of course, this requires
the condition that r  n1). Further assume that polynomial Xr  is
irreducible modulo p where p is a prime divisor of n and r > 4 log2
n.
Show that the test can be modified to simply testing:
(X + 1)n
