#ATTENDANCE QUIZ FOR LECTURE 14 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p24
#with an attachment called
#p24FirstLast.txt
#(e.g. p24DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Dec. 8, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH, BY THE ANSWER

Question 1: Write down all the integer partitions of 7 by hand.
Answer 1:
7
6+1
5+2
4+3
3+2+2
3+3+1
4+2+1
5+1+1
2+2+2+1
3+2+1+1
4+1+1+1
2+2+1+1+1
3+1+1+1+1
2+1+1+1+1+1
1+1+1+1+1+1+1

Question 2: Write down the set of partitions of 7 into distinct even and odds parts/

Answer 2: 7 odd parts and 7 even parts

Question 3: What is the A number of 1, 2, 3, 5, 7, 11, 15, 22 in the OEIS?

Answer 3: A000041		a(n) is the number of partitions of n (the partition numbers).

Question 4: who wrote the classic book on the tehory of partitions? What is his birthdate?

Answer 4: George andrews - born - December 4, 1938

Question 5: What is the A number?
Answer 5:	A09 Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.

Question 6:
What is the A number of 1, 1, 1, 2, 2, 3, 3, 4, 5, 6

Answer 6: A000607		Number of partitions of n into prime parts.

Question 7:Whose theorem is it that these above two sequences are the same?

Answer 7: Euler

Question 8: Is it in the OEIS? What is the A number?

Answer 8:A071734		a(n) = p(5n+4)/5 where p(k) denotes the k-th partition number.

Question 9: 

Does there exist a k between 0 and 6 such that seq(pn(7*n+k)/7, n=1..60) is an integer sequence
What is the A number if it exists

Does there exist a k between 0 and 10 such that seq(pn(11*n+k)/11, n=1..60) is an integer sequence
What is the A number if it exists

Question 10:

Why should Dr. Z from now on make you watch lectures before recitations?

Answer 10:
So that people can come to the recitations if they did not understand anything.