The 3-Part of Class Numbers of Quadratic Fields
... Q( D) for g ≥ 3 has remained unsolved. This thesis provides three nontrivial bounds for h3 (D), giving the first improvement on the previously known trivial bound h3 (D) |D|1/2+ . This thesis approaches the problem via analytic number theory, phrasing the problem of bounding h3 (D) in terms of co ...
... Q( D) for g ≥ 3 has remained unsolved. This thesis provides three nontrivial bounds for h3 (D), giving the first improvement on the previously known trivial bound h3 (D) |D|1/2+ . This thesis approaches the problem via analytic number theory, phrasing the problem of bounding h3 (D) in terms of co ...
104 Number Theory Problems
... students’ number-theoretic skills and techniques. The first chapter provides a comprehensive introduction to number theory and its mathematical structures. This chapter can serve as a textbook for a short course in number theory. This work aims to broaden students’ view of mathematics and better prep ...
... students’ number-theoretic skills and techniques. The first chapter provides a comprehensive introduction to number theory and its mathematical structures. This chapter can serve as a textbook for a short course in number theory. This work aims to broaden students’ view of mathematics and better prep ...
Congruence Notes for Math 135
... Table 1: Multiplication and Addition for odd and even integers. We have divided the natural numbers into two sets: • the even integers 0, 2, 4, 6, . . . • the odd integers 1, 3, 5, 7, . . . and observed that any two numbers chosen from the same set behave alike with regard to whether the answer to a ...
... Table 1: Multiplication and Addition for odd and even integers. We have divided the natural numbers into two sets: • the even integers 0, 2, 4, 6, . . . • the odd integers 1, 3, 5, 7, . . . and observed that any two numbers chosen from the same set behave alike with regard to whether the answer to a ...
pseudoprime or a Carmichael number
... s log x, and denote by r,, r_, . . . the primes for which (r;-1) A . It is easy to see that A x' , for sufficiently large x . It is reasonable to expect that for ii (log x)` " there are more than c ;,, : -r(u) (c,,,== c,,,(c,..)) is not exceeding u (though this will probably be very hard to prove). ...
... s log x, and denote by r,, r_, . . . the primes for which (r;-1) A . It is easy to see that A x' , for sufficiently large x . It is reasonable to expect that for ii (log x)` " there are more than c ;,, : -r(u) (c,,,== c,,,(c,..)) is not exceeding u (though this will probably be very hard to prove). ...
Factorization of Natural Numbers based on Quaternion Algebra
... The factorization problem has been challenging generations over the centuries. Since we still do not know if there exists a deterministic algorithm that computes a factor of a positive integer n in polynomial time, there is lot of research into the question ”Is factorization NP-complete?” And becaus ...
... The factorization problem has been challenging generations over the centuries. Since we still do not know if there exists a deterministic algorithm that computes a factor of a positive integer n in polynomial time, there is lot of research into the question ”Is factorization NP-complete?” And becaus ...
Problem Solving: Consecutive Integers
... If you count by twos beginning with any even integer, you obtain consecutive even integers. For example, ...
... If you count by twos beginning with any even integer, you obtain consecutive even integers. For example, ...
single pdf
... 13. What is the sum of the factors of 1572? 14. There are 4 different types of monitors, 5 different CPU’s, and 3 different types of printers that can be purchased. Two of the CPU’s are not compatible with one of the monitors. How many different systems can be purchased? 15. A committee of 3 people ...
... 13. What is the sum of the factors of 1572? 14. There are 4 different types of monitors, 5 different CPU’s, and 3 different types of printers that can be purchased. Two of the CPU’s are not compatible with one of the monitors. How many different systems can be purchased? 15. A committee of 3 people ...
PUTNAM TRAINING PROBLEMS, 2011 Exercises 1. Induction. 1.1
... row. By turns each of them takes one token from one of the piles and adds at will as many tokens as he or she wishes to piles placed to the left of the pile from which the token was taken. Assuming that the game ever finishes, the player that takes the last token wins. Prove that, no matter how they ...
... row. By turns each of them takes one token from one of the piles and adds at will as many tokens as he or she wishes to piles placed to the left of the pile from which the token was taken. Assuming that the game ever finishes, the player that takes the last token wins. Prove that, no matter how they ...
