Find mod(4^(1001)+1001!,7).
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 (5/7) mod 8
4. Find each of these values: (a) (177 mod 31 + 270 mod 31) mod 3 (b) (177 mod 31 · 270 mod 31) mod 31
What is the order of an element of a group, find the order of 4 (mod 7). And what is a primitive element mod n, is 5 a primitive element modulo 19? Verify or refute it.
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
3. Find a div m (meaning find quotient and remainder) and a mod m when: (a) a = 10299, m = 999 (b) a = 123456, m = 1001 (c) a = −111, m = 99 (d) a = −1000, m = 101
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 (i) 2^25 mod 21, (ii) 7^66 mod 120 and (iii) the last two digits of 1 + 7^162 + 5^121 * 3^312
Math 1001 264 MOD Quantitative Skills and Reasoning Test: Test 1_(CH 1, CH9, CH10) This Question: 1 pt 22 of 25 (11 comple Use the English and metric equivalents to the right, along with dimensional analysis, to convert the given measurement to the unit indicated 217 mi to km km Round to the nearest hundredth as needed)
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