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CS681: Endterm Examination Maximum Marks: 50

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
r Zn is a primitive rth root of unity (of course, this requires
the condition that r | n-1). Further assume that polynomial Xr - is
irreducible modulo p where p is a prime divisor of n and r > 4 log2
Show that the test can be modified to simply testing:
(X + 1)n


Source: Agrawal, Manindra - Department of Computer Science and Engineering, Indian Institute of Technology Kanpur


Collections: Computer Technologies and Information Sciences