Question Lisiaiq a modular arithmetic Compute the following a) –3 mod 5; 9' mad 26; 2t...
2. Use modular arithmetic rules to find out the following: Use the rule: (a*b) mod x -( (a mod x) (b mod x)) modx Find out: (97)49 mod 119 Hints: 49 can be written as: 49-32 16+1 Try finding out 97 mod 119 Then, 972 mod 119, then 974 mod 119 etc.
Modular arithmetic topic: 97=2 mod 5 and 144=4 mod 5. Hence (97^3+144^2=2^3+4^2=8+16) . so the conclusion is 97^3+144^2=4 mod 5(this is the answer but I have no idea) . I don't quite understand here......
Discrete Mathematics. Question 2: (a) Use modular arithmetic to find 1040 mod 210. Show your working. (b) An RSA cryptosystem uses public key pq = 65 and e = 7. Decrypt the ciphertext 57 9 and translate the result into letters of the alphabet to discover the message.
Answer the following questions using modular arithmetic a) Determine if 5201,001 −2 is divisible by 3. b) Determine all of the zeros of the polynomial p(x) = x2 + x mod6. c) Show that if a2 + b2 = c2, then a ≡ 0,2 mod 4 or b ≡ 0,2 mod 4
Please answer question 3 Find all (infinitely many) solutions of the system of congruence's: Use Fermata little theorem to find 8^223 mod 11. (You are not allowed to use modular exponentiation.) Show that if p f a, then a^y-2 is an inverse of a modulo p. Use this observation to compute an inverse 2 modulo 7. What is the decryption function for an affine cipher if the encryption function is 13x + 17 (mod 26)? Encode and then decode the...
9. Use the construction in the proof of the Chinese remainder theorem to find a solution to the system of congruences X 1 mod 2 x 2 mod 3 x 3 mod 5 x 4 mod 11 10. Use Fermats little theorem to find 712 mod 13 11. What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 (4xn + 1) mod 7 with seed xo 3? 9. Use the construction in the proof of the Chinese...
Arithmetic Dynamics 1. Compute the cycle length of mltiplication by mod & a-3 -7 6-7 a7, 6-12 a17. 6-25 a2. 6- 2 a-5 Arithmetic Dynamics 1. Compute the cycle length of mltiplication by mod & a-3 -7 6-7 a7, 6-12 a17. 6-25 a2. 6- 2 a-5
5. (a) Show that 26 = 1 mod 9. (b) Let m be a positive integer, and let m = 6q+r where q and r are integers with 0 <r < 6. Use (a) and rules of exponents to show that 2" = 2 mod 9 (c) Use (b) to find an s in {0,1,...,8} with 21024 = s mod 9.
probelms 9.1 9 Modular arithmetic Definition 9.1 Let S be a set. A relation R = R(,y) on S is a statement about pairs (x,y) of elements of S. For r,y ES, I is related to y notation: Ry) if R(x,y) is true. A relation Ris: Reflexive if for any I ES, R. Symmetric if for any ry ES, Ry implies y Rr. Transitive if for any r.y.ES, Ry and yRimply R. An equivalence relation is a reflexive, symmetric and...
3. 11,7,3,-1,-5-4-9-13-11-2 a) arithmetic b) a = 11 + (8 - 1) = 4 c) -21 10.4 For questions 1-5, a. Determine if the sequence is arithmetic or geometric. b. Write a formula for the nth term in the sequence. c. Find the 9th term in the sequence, using the formula from part b.