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MATH 4161	NUMBER THEORY	Section 001
Instructor: Gábor Hetyei		Last update: April 24, 2002

Homework assignments

Disclaimer: The information below comes with no warranty. If, due to typocraphical error, there is a discrepancy between the exercise numbers announced in class and the numbers below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise number shows up below, I will allow you extra time to hand in the exercise whose number was announced in class. If, however, exercise numbers are missing because this page is not up to date, it is your responsability to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date.

Date due Problems:

Monday April 29, 2002 10.2/2ac,3,4, 13.1/1,2, give a closed formula for the Lucas numbers (in analogy with the Binet formula, for the definition of Lucas numbers see 13.2/17), give a closed formula for the sequence a₁,a₂, ..., defined by a₁=3, a₂=5 and a_n+1=a_n+2a_n-1.

Monday April 22, 2002 9.3/3b,4, 9.4/2b

Monday April 15, 2002 9.2/1ace,2c,4b 9.3/1ac,5a

Monday April 1, 2002 8.3/1ab,2a,3 8.4/1.
We will have a review on Monday and Test 2 on April 3!!!

Monday March 25, 2002 7.4/2,5ac,6, 8.1/1c (create the whole table of indices and orders), 2a, 8.2/1a, 4a, 8a.

Monday March 18, 2002 7.2/1,3,6,8, 6.2/8a (use 6.2/3) 6.3/6,8b

Monday March 11, 2002 6.2/1a,2,4ac,7b, 6.3/2abc,5a

Monday February 25, 2002 4.4/4d,7,15c, 6.1/6,7,8,9
Bonus: Calculate the first four or five coefficients in the expansion of (1+x)^1/2, and use them to estimate the value of the square root of 1/2.

Monday February 18, 2002 5.3/1,2a,6a, 5.4/1b,7

Monday February 11, 2002 4.3/1bc,3,4b,5a, 4.4/1bc, 4a,5.

Monday February 4, 2002 3.1/6bc, 3.2/4ab,5, 4.2/1b,2.

Monday January 28, 2002 2.4/1ac, 2b, 3.1/1,3bc; in the solution of 2.3/1 express the gretast common divisor as a linear combination of the original numbers.

Wednesday January 23, 2002 2.1/2,3ac,8 2.2/1,3,4a,12 2.3/1,4b.
Bonus: Consider the Euclidean Algorithm presented in the proof of Theorem 2.7. Express r₅ as a linear combination of a and b.

Monday January 14, 2002 1.1/1b, 1c,3,9, 1.2/1b,2.
Bonus: Assuming the Principle of Finite Induction, prove the Well-Ordering Principle.

Date due	Problems:
Monday April 29, 2002	10.2/2ac,3,4, 13.1/1,2, give a closed formula for the Lucas numbers (in analogy with the Binet formula, for the definition of Lucas numbers see 13.2/17), give a closed formula for the sequence a₁,a₂, ..., defined by a₁=3, a₂=5 and a_n+1=a_n+2a_n-1.
Monday April 22, 2002	9.3/3b,4, 9.4/2b
Monday April 15, 2002	9.2/1ace,2c,4b 9.3/1ac,5a
Monday April 1, 2002	8.3/1ab,2a,3 8.4/1. We will have a review on Monday and Test 2 on April 3!!!
Monday March 25, 2002	7.4/2,5ac,6, 8.1/1c (create the whole table of indices and orders), 2a, 8.2/1a, 4a, 8a.
Monday March 18, 2002	7.2/1,3,6,8, 6.2/8a (use 6.2/3) 6.3/6,8b
Monday March 11, 2002	6.2/1a,2,4ac,7b, 6.3/2abc,5a
Monday February 25, 2002	4.4/4d,7,15c, 6.1/6,7,8,9 Bonus: Calculate the first four or five coefficients in the expansion of (1+x)^1/2, and use them to estimate the value of the square root of 1/2.
Monday February 18, 2002	5.3/1,2a,6a, 5.4/1b,7
Monday February 11, 2002	4.3/1bc,3,4b,5a, 4.4/1bc, 4a,5.
Monday February 4, 2002	3.1/6bc, 3.2/4ab,5, 4.2/1b,2.
Monday January 28, 2002	2.4/1ac, 2b, 3.1/1,3bc; in the solution of 2.3/1 express the gretast common divisor as a linear combination of the original numbers.
Wednesday January 23, 2002	2.1/2,3ac,8 2.2/1,3,4a,12 2.3/1,4b. Bonus: Consider the Euclidean Algorithm presented in the proof of Theorem 2.7. Express r₅ as a linear combination of a and b.
Monday January 14, 2002	1.1/1b, 1c,3,9, 1.2/1b,2. Bonus: Assuming the Principle of Finite Induction, prove the Well-Ordering Principle.