MATH 115A SOLUTION SET III JANUARY 27, 2005 (1) Use Fermat's Little Theorem to verify that 17 divides 11104 + 1. Solution: Working modulo 17, we have that 11104 (112 )52 252
5 10
(mod 17) (mod 17) (mod 17)
(mod 17)
10
(2 ) 22 (-2) 4 44
(mod 17)
16 (mod
Practice Sheet 2
1. Find an integer that leaves a remainder of one when divided by either 2 or 5 but that is divisible by 3.
Using the fact that the congruences
x a ( mod n )
and
x b ( mod m ) admit a simultaneous
solution iff gcd ( n , m )( ab) , find ou
All Quiz Questions
1. Find the remainder using modular exponentiation when 31001 is divided
by 17
2. Decide whether 250 and 4165 belong to same residue class modulo 7 or not
3. Define order of an integer and find order of 5 modulo 19
4. Give that how many
Math 116 Number Theory
with Travis Kelm
Homework #2
Divisibility and Primes
Spring 2007
CSU - Fresno
Solutions
In your solutions you must explain what you are doing using complete sentences.
Section 1.5
Exercise 8: Are there integers a, b, and c = 0 such
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The Web is not the Internet. The Web runs on top of
the Internet, in a sense. The Web is the collection of
HTTP servers that hold and process web sites we see.
The Internet is the coll
Understanding Enterprise
Network Architecture
Enterprise Network Architecture
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Perimeter
Problem 1:
In the three-phase converter of Figure 1, VLL=460V at 60 Hz and Ls= 25uH.
Figure 1.
1. Calculate the commutation angle u if Vd=525V and Pd =500kW.
2. After you calculate commutation angel, calculate Vd for the same load, VLL and
frequency, assu