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Math 315; Homework # 5
Due March 4, 2015
1. (Exercise 18.1) Decode the following message, which was sent using the modulus m = 7081 and the exponent k = 1789. (Note that you will rst need to factor
m.)
5192, 2604, 4222
2. (Exercise 20.3) A number a is cal
MATH 315; HOMEWORK # 1
Due Jan 19, 2015
1. (page 11, Exercise 1.3) The consecutive odd numbers 3,5, and 7 are all primes.
Are there innitely many such prime triplets? That is, are there innitely many
prime numbers p so that p + 2 and p + 4 are also primes
Assignment #1 STA457H1S/2202H1S
due Wednesday February 3, 2016
Instructions: Students in STA457S do problems 1 through 3; those in STA2202S do all 4 problems.
1. Daily Japanese yen/US dollar exchange rates (JPY/USD) from Dec. 1, 1978 to Apr.29, 2005
are g
MATH 315; HOMEWORK # 2
Due February 5, 2016
1. (Exercise 6.4 (c) Find all integer solutions of 155x + 341y + 385z = 1. [Hint:
gcd(341, 385) = 11. Write the equation as 155x + 11(31y + 35z) = 1. First solve
the equation 155x + 11u = 1 and then solve 31y +
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MATH 315; HOMEWORK # 1
Due Jan 22, 2016
1. (similar to Exercise 3.3, page 24) Find a formula for all of the points on the
hyperbola x2 2y 2 = 1 whose coordinates are rational numbers.
2. (similar to Exercise 3.4, page 24) The curve y 2 = x3 + 17 contains
MATH 315; HOMEWORK # 3
Due Feb. 4, 2015
1. (Exercise 11.2) (a) If m 3, explain why (m) is always even.
(b) (m) is usually divisible by 4. Describe all of the ms for which (m) is
not divisible by 4.
2. (Exercise 11.5 (a) Find x that solves the simultaneous
MATH 315; HOMEWORK # 4
Due Feb. 25, 2015
n
1. (Exercise 14.2) Let Fn = 22 + 1, so, for example, F1 = 5, F2 = 17, F3 = 257
and F4 = 65537. Fermat thought that all of Fn s might be prime, but Euler showed
in 1732 that F5 factors as 641 6700417, and in 1880
UNIVERSITY OF TORONTO
DEPARTMENT OF MATHEMATICS
MAT315H1S
Introduction to Number Theory
Winter Semester 2015
Instructors:
Lectures:
Textbook:
Dr. Henry Kim, BA 6250, 416-978-4443
MWF9
A Friendly Introduction to Number Theory, 4th ed.
by Joseph H. Silverma
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