EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 1




MAT315
UTSG
Tian Jin
2022.02.04
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 2




EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 3








This complementary study package is provided by Easy Education Inc. and its affiliated
mentors. This study package seeks to support your study process and should be used
as a complement, NOT substitute to course material, lecture notes, problem sets, past
tests and other available resources.

We acknowledge that this package contains some materials provided by professors
and staff of the University of Toronto, and the sources of these materials are cited in
detail wherever they appear.

This package is distributed for free to students participating in Easy Education’s review
seminars and are not for sale or other commercial uses whatsoever. We kindly ask you
to refrain from copying or selling in part or in whole any information provided in this
package.

Thank you for choosing Easy Education. We sincerely wish you the best of luck in all of
your exams.



Easy Education Inc.



Disclaimer
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Ac
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 4


Table of Contents

l 2017 Fall Past Test
l 2018 Fall Past Test
l 2019 Fall Past Test
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 5


Past Exams_2018 Fall

Q1, Power of 23 in 2525!

































EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 6


Q2, 5!""""#" mod23


EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 7


Q3, x=2mod7
X=5mod9
X=1mod13






EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 8


Q4, a and b are relatively prime, d|ab, show d=gcd(a,d)gcd(b,d)




EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 9


Q5, State Fermat Little Theorem and prove it.





EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 10


Q6, Fibonacci number, Fn
m=aFn+bFn-1


EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 11


Q7, pseudoprime base a?
Carmichael number?
Strong pseudoprime base a?

Is N prime?
Is N pseudoprime base 2,3,5,7,11?
Is N strong pseudoprime base 2,3,5,7,11?


EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EASY EDUCATION | MAT315 WINTER 2021-2022
TT1 REVIEW P2

导师：TIAN JIN | EASY EDUCATION UTSG 校区 12


Q8, n=ar…a1a0 is divisible by 11 iff a0-a1+…ar=0 mod 11




EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324
EZ Aca
demy
ZhuoY
izhao
98324