Find (5/7) mod 8
8-7. Find the smallest positive integer a such that 5:13 +13n" + a(9) = 0 (mod 65) for all integers n.
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
1. Find the mean, mod, median, and standard deviation of the following data: 5, 6, 7, 8, 9,8,7,8 Based on these results, check whether the value of 10 is usual?
7. Prove or disprove: If we know that 2X +6=4 (mod 8), then X +3 = 2 (mod 8). 8. Prove or disprove: If we know that 2X+6 = 4 (mod 7), then X+3 = 2 (mod 7). 9. Let S be the set {311, 254, -172,45,2019, 111,3}. Find a subset T such that the sum of the elements in divisible by 7
Solve the following for x 4x ≡ 7 (mod 19) 6x ≡ 8 (mod 31) 9x ≡ 7 (mod 16)
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 additive inverse of the following value mod m. 16. 7 mod 9 17. 4 mod 12 18. 63 mod 30 19. 222 mod 3
Find mod(4^(1001)+1001!,7).
Evaluate the following: (i) 7^1300 mod 8, (ii) 72^36 mod 15, (iii) 15^546 mod 17. You may not use a calculator or computer - do this by hand, and show your computations.
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...