Problem Sheets (pdf), MP313 Number Theory III, Semester 2, 1999
Problem Sheet 1
(divisibilty, gcd, Euler's function)
Problem Sheet 2
(congruences, multiplicative functions)
Problem Sheet 3
(quadratic residues, primitive roots)
Assignment 2
(Solving x
4
-1 (mod p), x
2
-3 (mod p), ord
p
(-x) in terms of ord
p
x)
Problem Sheet 4
(Legendre symbol)
Holiday Problem Sheet
(elements of even order (mod p), Jacobstahl's theorem, criterion for p=x
2
+1)
Assignment 3
(1048601=x
2
-2y
2
, solving x
2
35 (mod 1201) by Tonelli's method)
Problem Sheet 6
(continued fraction expansion of quadratic irrationalities)
Problem Sheet 7
(p-adic integers)
Return to MP313 page
KRM Tue 28th May 2004
-1 (mod p), x2 -3 (mod p), ordp(-x) in terms of ordpx)
35 (mod 1201) by Tonelli's method)
-1 (mod p), x2 -3 (mod p), ordp(-x) in terms of ordpx)
35 (mod 1201) by Tonelli's method)