Find mod (2^1003+1003! ,5)
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 (5/7) mod 8
5. (20 points) Solve the system of congruences x (mod 13) and 11 (mod 24). Find the smallest nonnegative integer solution to the system.
1. Are the following expressions true or false? 2550 (mod 5) 3353 (mod 11) 1856 (mod 3) 8058 (mod 9) 3859 (mod 4) True True True True True False False False False False 2. Apply Euclid's algorithm to find gcd (424762, 28101). Calculations: gcd (424762, 28101) = 3. Record the number 1800 as the product of primes. 1800 =
Find (i) 2^25 mod 21, (ii) 7^66 mod 120 and (iii) the last two digits of 1 + 7^162 + 5^121 * 3^312
Find the smallest positive solution and the general solution to the system x ≡ 1 (mod 3), x ≡ 2 (mod 5) and x ≡ 3 (mod 7). Exercise 2 (5 points Find the smallest positive solution and the general solution to the system ΧΞ2 (mod 5) and r Ξ 3 (mod 7). 1 (mod 3),
4. Find each of these values: (a) (177 mod 31 + 270 mod 31) mod 3 (b) (177 mod 31 · 270 mod 31) mod 31
6.) Find (i) 225 mod 21, (ii) 766 mod 120 and (iii) the last two digits of 1 + 7162 + 5121. 3.12. 6. Find + (iii) the last two digits of 1 + 7162 +5121.3.12 (i) 225 mod 21, (ii) 766 mod 120 Answ ven 6. (i) 225 = 2 mod 21; (ii) 766 = 72 = 49 mod 1 20. (iii) °(100) = 40. So the last two digits of 7162 are 49. Note that, since (5, 100)...
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......
Find all solutions to the following linear congruences. (15 points) (a) 2x ≡ 5 (mod 7). (b) 6x ≡ 5 (mod 8). (c) 19x ≡ 30 (mod 40). Show all the steps taken in neat English to receive a positive review