Mod

Lemma: If p > 3 is prime, then either p = 1 (mod 6) or p = 5 (mod 6). Proof: The residue classes modulo 6 partition Z, so any z in Z satisfies a congruence z = n (mod 6) where n is in {0,1,...,5}. z is divisible by 6 if n = 0, 2 if n = 2, 3 if n = 3, and 2 if n = 4. These cases cover the primes z = 2 and z = 3; if z > 3 is prime, it follows that n = 1 or n = 5, i.e., z = 1 (mod 6) or z = 5 (mod 6). Now suppose there are only finitely many primes congruent to 5 modulo 6, say p_1, ...,…

Mia Lindsey Intro to Art 100 Mod 2 Worksheet 2 Instructions: Compare and contrast art created as a social activity and as a singular creative act. Include artist image and proper citation. (Artists name, date, medium, current location if applicable.) • What are the differences? • Why are they important? • Do their functions ever overlap? How? Singular Creative Act: Still life painting: Adriaen Coorte’s Strawberries in a Wan Li Bowl: 1704 Oil Painting: Current location: Unknown Social Activity:…

Leadership Kathy Dunlap Bethel University MOD 310 April 24, 2017 Kameke Payne Leadership No one theory of leadership has ever been accepted by all, but the common thought of leadership is that it is an influence process, occurs within a group, involves goals, and attainment. Some people think leaders are born with a trait that innately makes them leaders, while others theorize that it is a characteristic of an individual, but we have learned that leaders are a product of their…

1960s The Decade that Shook Britain by Kimberly Watson, expresses the reason subcultures like mods and rockers were initiated and why they became so accepted. The mod and rocker movement started as a rebellion for the youth of Britain to find their own…

Reflections. The first instrument used to collect data is the TTT PT Mod 3 reflections which are submitted by each training participant at the end of the TTT PT Mod 3 training session. Teachers are asked to submit two statements that measure teachers’ attitude and intentions to use the TTT PT Mod 3 technology tool. The teachers are asked to submit a reflection statement on the benefits of the technology tool presented in the training; and a reflection statement of a plan outlining at least two…

exists a unique x ∈ Z with 0 ≤ x < N such that x ≡ a1 mod n1 x ≡ a2 mod n2 . . . x ≡ ak mod nk Stated another way, Z/NZ ∼= Z/n1Z×· · ·×Z/nkZ given by x mod N 7→ (x mod n1, . . . , x mod nk) is a ring homomorphism. Proof. Let N = n1n2 . . . nk, yi = N ni for all i = 1, 2, . . . , k, and zi = y −1 i mod ni . Note that y −1 i mod ni exist since yi and ni are coprime by construction. Notice that when j 6= r, yjzj ≡ 0 mod nr and when j = r, yjzj ≡ 1 mod nr. Then x = X k i=1 aiyizi (7) satisfies…

Then the key (Key1Q)Q^-1 mod n by applying Q-1 by is calculated by sender A and it must be equal to Key1 because Q.Q-1 = 1 mod (n-1). Therefore, although so we can say a wrong session key is obtained by sender and intruder cannot compute the same wrong session key, and the sender A have to trust on it. So it is proved that verification…

Introduction Cryptography can be defined as the process of encrypting and decrypting data in order to keep the information protected from anyone other than the two (or more) people involved in the communication. Preventing unauthorized users from being able to read the information exchanged over an insecure channel, i.e. maintaining ‘privacy’ is one serious cryptographic problem, which is why it is essential for the communicating parties to share a key that is unknown to others. This key…

7-1 to 7-4 can be represented mathematically using modular arithmetic or arithmetic modulo n. Definition 7-1: Two integers a and b are said to be congruent modulo n, where n is a natural number, if (a-b)/n is an integer. In this case, we write a≡b mod…

would record the user and then post my proof on the forums and then I would talk to higher staff members and other helpers to see if they agree that the user is hacking and then I would inform a mod + to see if they could ban them. As Helper Record user and then post my proof on the forum and on youtube As Mod+ Record User and post on the forums and have other staff members agree that he is hacking. Advertising: Advertising is when someone put a server ip in chat to try and get more people…