Hi, I'm a little lost as to how to use Fermats Little Theorem to simplify.
2-100 mod 19
Since 19 is prime then that should mean that 218 mod 19 = 1.
So,
2-100 mod 19:
= 218 * -5 + (-10) mod 19
=(218)-5 * 510 mod 19
= 1-5 * 510 mod 19
= 510 mod 19
I need some assistance after this part...
Haha of course. Yep, I plugged in 40 back into the original equation and I got
3x + 50 = 11 mod 53
3(40) + 50 = 11 mod 53
120 => 11 mod 53
However, I have another question
Say you're given something like this
"Solve 7x + 2 = 2-100 in F19"
I tried doing this the same way as...
Hi micromass,
So
3x = 14 mod 53
18 * 3x = 18 * 14 mod 53
Is it safe to assume that 18 * 3x = x since 3*3-1 = 1?
therefore
x = 18 * 14 mod 53
= 252 mod 53
= 40 mod 53
Is this the correct approach?
-Thanks
Hi icystrike,
I'm not sure what you mean.
After getting all the equations you just continue to use back substitution, right?
I'm having trouble simplifying the expression after using back substitution.
For example in the text
gcd(330,156):
330 = 156 * 2 + 18 which implies 18 = 330...
Extended Euclidean Algorithm(Example Run-Through)
Homework Statement
I need help tracing through an example of Diophantine Equations.
The question:
Find integers x and y such that 37x + 29y = 1.
Homework Equations
The use of Euclidean Algorithm is required.
The Attempt at a...
Homework Statement
I have a basic question regarding the truth table for decoders and encoders.
Let's say for a 3 to 8 line decoder with inputs x y z and outputs F0...F7
The truth table is
x y z | F0 F1 F2 F3 F4 F5 F6 F7
0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0...
1. Homework Statement
1.(a) How many 4 digit hexadecimal numbers can be formed using the hexadecimal digits 1. 5, 6, 9, A, C?(Repetition is allowed)
(b) How many four digit hexadecimal numbers with distinct digits can be formed using the hexadecimal digits above?
(c) What is the...
Homework Statement
Using the Arctangent formula
pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.Homework Equations
The power series of arctangent(x) is = x − x^3/3 + x^5/5 − x^7/7 + x^9/9...
The Attempt at a Solution...
Hi sorry for the late reply,
I am still somewhat confused about how to approach this question. So far this is how I've startend it.
Let j = K+1/K+2
Therefore when k = 0,
j = 1/2
and when K = n - 1,
j = (n-1) + 1 / (n-1 ) + 2
j = n
So I introduce another variable for the other...
Homework Statement
Rewrite the following expression as a single product.
Hint: Perform a change of variable first.
Homework Equations
The Attempt at a Solution
I looked at the example from the book regarding a change of variable. They first started out by calculating the upper and lower...
Oh I see now.
so
5 mod 2 = 1
c mod 2 = 1
therefore c can be 5, 7, 9, 11, etc. since 7/2 has a remainder of 1 and 9/2 has a remainder of one.
Similarly,
3 mod 3 = 0 so;
d mod 3 = 0
therefore d can be 3, 6, 9, 12 etc.
So would 4 ordered pairs be;
(5,3), (7,6), (9,9)...
Hi mark thank you for your reply,
So "a mod b" is always going to produce an integer "b - 1"?
So for part a here is what I have so far;
a == c mod 2
=> a mod 2 = c mod 2
we let a = 5
so 5 mod 2 = c mod 2
Is this correct so far?
-Thank you in advance.
Homework Statement
\forall (a,b), (c,d) \in (Z^2), (a,b)D(c,d) \leftrightarrow a\equiv c\mod\2\and\b\equiv d mod 3
*edit* Sorry the b = d mod 3 is all part of the same line.
(a) List four elements of the equivalence class [{5,3}]
(b) How many equivalence classes of D are there in total...
hi, sorry for the late reply.
Solving for dx I got
dx= du/(Sec^2(3x)) x 3
So
Sec^2(3x)e^u du/sec^2(3x) x 3
sec^2(3x) cancel each other out?
so I'm left with
e^u(du)(1/3) = 1/3e^u(du)
so 1/3e^(tan(3x))+C?
Is my approach correct?
-Thank You