4. Find each of these values: (a) (177 mod 31 + 270 mod 31) mod 3 (b) (177 mod 31 · 270 mod 31) mod 31
a) 177 mod 31 = 22
270 mod 31 = 22
(177 mod 31 + 270 mod 31) mod 3 = (22 + 22) mod 3 = 44 mod 3 = 2
b) (177 mod 31 - 270 mod 31) mod 3 = (22 - 22) mod 3 = 0 mod 3 = 0
4. Find each of these values: (a) (177 mod 31 + 270 mod 31) mod 3...
PROBLEM 5 [points: 10] Find values: a) 19mod 3 = b) -19 mod 3 = c) -20 mod 3 = d) I-7.6]= e) I-761 =
Elucidean Algorithm. Q 4. For each of the following equations, find a solution z Z or prove that no solution z E Z exists (a) 7x 13 mod 83 mod 624; 11 (b) 25x + 3 (c) 36r 1 mod 87. 12 marks In all cases, explain your reasoning. Q 4. For each of the following equations, find a solution z Z or prove that no solution z E Z exists (a) 7x 13 mod 83 mod 624; 11 (b)...
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...
Find the additive inverse of the following value mod m. 16. 7 mod 9 17. 4 mod 12 18. 63 mod 30 19. 222 mod 3
Abstract Algebra based off of John B. Fraleigh's textbook 3. Find 473 (mod 15) 4. Find all integer solutions to the equation 21x 28 (mod 70). 5. Classify the group Z15 xZ4/K(3, 2)) using the fundamental theorem of finitely generated abelian groups.
the integer x such that 5 3 (mod 7) 57 (mod 61) e linear congruence 31
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Using the Extended Euclidean Algorithm, find the multiplicative inverse of: 31 mod 3480
7. Given cos 20 = --and 180° <0 < 270°, find values of sino and cose.
Find mod(4^(1001)+1001!,7).