#ATTENDANCE QUIZ FOR LECTURE 25 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p25
#with an attachment called
#p25FirstLast.txt
#(e.g. p25DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Dec. 11, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 4

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

QUESTION #1:

Who is the most prolific mathematician of all time? 

ANSWER:

Leonhard Euler, 

According to https://link.springer.com/chapter/10.1007/978-81-322-0767-2_10#:~:text=Leonhard%20Euler%20is%20one%20of,most%20prolific%20mathematician%20in%20history..

QUESTION #2:

Is 2,4,6,10,16,24,36,52,74,104,144,198,268,360,480,.. in the OEIS?

ANSWER:

Yes, its A-number is A098151
Description: Number of partitions of 2n prime to 3 with all odd parts occurring with even multiplicities. There is no restriction on the even parts.

QUESTION #3:

By hand find BZ([[5,2,1,1], -1]). Check that it is the same on the computer.

ANSWER:

We have, L = [5,2,1,1], j = -1, t = 4.
t+3*j = 4 - 3 = 1 
L[1] = 5.
Since t+3*j < L[1], 

Then, Phi(L) = (3,2,2,1,1,1)
Running, BZ([[5,2,1,1], -1]) in maple, we get BZ([[5, 2, 1, 1], -1]);
[[3, 2, 2, 1, 1, 1], 0]

This matches our calculation.

QUESTION #4:

What is BZ([[100$20], 0])?

ANSWER:

Running in Maple, we get:
[[101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 101, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 1]