If x ≅ y (mod n) and q ≅ z (mod n); then (x +q) ≅ (y + z) (mod n):, i know how to prove this, my question is if we wanted to prove it holds for (x + q) ≅ (y + z) (mod 2n): would this be true or false ?, if true how would i show it ? i know it should be simple but im confused.
How can you show that 3^54321 - 6 is a multiple of 7? I know you would use modular arithmetic (and maybe the Euclidean algorithm?), but I don't know how to go about doing that. Any help would be greatly appreciated!
First problem
Let n ∈ N and let Z denote the set of equivalence classes for the relation of congruence modulo n. Let n ∈ Z. Define the order of the element [a]n ∈ Z to be the smallest number k such that :
k * [a]n := [a]n + [a]n+....+[a]n = [0]n
where the number of terms in the sum is k.
(a)...
I am trying to find the inverse of 314(mod 7). I have no idea what I am doing wrong..
What I do is:
1) find if gcd(314,7) = 1. Yes!
314 = 7*44 + 6
7 = 6*1 + 1
6 = 1*6 + 0
2) Now to find inverse of 314 I do this:
1 = 7-6
1 = 7 - (314 - 7*44)
1 = 7*45 - 314
And inverse of 314 is -1... What am...
Hi,
I am currently working on modular arithmetic and recently I have been investigating on the effects of
exponentiation on the system.It will be helpful if someone can share some ideas on the following problem.
According to the division algorithm:
a= nQ+r,
where a is the dividend,n is the...
1/192 = k mod7
I ran this through Wolfram Alpha and got the answer k=5
I assume that this is because
(192 * 5)/7 has a remainder of 1 (is this correct?)
Is there a good way of finding the 5 manually?
Thankyou.
I had a young person ask me about modular arithmetic on calculators.
I have had very little dealings with modular arithmetic and i didn't think it was a function on most calculators.
I found this online modular calculator but I am confused about how it works.
you enter the mod you want (m)-...
Does anyone know how to code Mathematica to solve modular problems? For example, say I want to solve 4x == 1 mod 5. My best guess was Mod[Solve[4x == 1, x], 5] but that only resulted in the response Mod[1/4, 5].
Thanks!
-Dan
Modular Arithmetic in Z:
Definition: a(modm) stands for the remainder when a is divided by m.
Definition: a(modm) + b(modm) is (a+b)(modm).
Definition: a(modm)xb(modm) is axb(modm).
Definition: a≡b(modm): a and b leave same remainder when divided by m
Theorem: If a≡b(modm) and c≡d(modm) then...
Hi, all
Let 1 + 1/2 + 1/3 .... +1/823 = r/823s
Without calculating the left hand side, prove that:
r ≡ s (mod8233)
I'm comfortable with modular arithmetic so that isnt the problem, I just dont really know how to begin....
Thanks!
so this is confusing, with mod arithmetic i see that you only need the remainder as an answer but i don't get how it is solved.
like
2 (equivalence sign) 4(mod 3)
(3+4)(mod 5)
I wanted to calculate What is the time complexity of this? I'm using a Java program?
Can anyone provide an explanation of the time complexity for the following calculations?
c= a * b mod n
and
m = a ^-1 * b mod n
I need any suggest.
my variable has 256 bits
I wanted to calculate What is the time complexity of this? I'm using a Java program?
Can anyone provide an explanation of the time complexity for the following calculations?
c= a * b mod n
and
m = a ^-1 * b mod n
I need any suggest.
Hi, I'm having trouble understanding how to evaluate the last digits of a given extremely large number. I know it has something to do with modular math, but I'm struggling with that still. If anyone could explain how to :
Find the last let's say 2 digits of 1402^1402. It would be very...