Use Fermat’s little theorem to find 2^938 mod 53
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...
the second part of the question can be solved by the chineses remainder theorem. Problem 4 (4pts) Recalled Fermat's little theorem: For every p, a € N, if p is a prime and pla, then -I = 1 mod p. Use Fermat's little theorem to find a = 71002 mod 13) and b =(71002 mod 41). Find an 3 (0 < < 13 x 41) such that r = a (mod 13) and 2 = b (mod 41).
7. Use Fermat's Little Theorem to find the remainders of each of the division problems a. 6150 -19 b. 937531.
Discrete structures please help!! Use Fermat's little theorem to find the remainder when 91000 is divided by 13. To get credit, use Fermat's little theorem and show how each step is done without using a calculator.
Use the convolution theorem to find the inverse Laplace transform of the given function. 3 53 (82 +9) 7"{276900}09-0
1. (a) Use the Extended Euclidean Algorithmn to compute the inverse of 10 mod 17. (b) Use your answer from (a) so solve the equation 10x = 8 mod 17. (c) Compute 1616 mod 17. You may assume that Fermat’s Little Theorem is true.
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) x = 2 (mod 7) x = 3 (mod 9) x = 4 (mod 11)
Problem 1 Use the Chinese remainder theorem, find all integers x such that: (20 pts) x = 1 (mod 5) r = 2 (mod 7) x = 3 (mod 9) I= 4 mod 11) Answer,
Problem 2. Find a primitive root for 53. Using this, you can devise a bijection α from the integers modulo 52 to the nonzero integers modulo 53 with the property that α(a + b) = α(a)· α(b) modulo 53. Explain. Does the law of exponents get involved at all? Note: For this to work right, you can think of integers mod 52 as {0, 1, 2, . . . , 51} or as any complete system of residues modulo 52,...
prove 10.8-10.9 LLLLLLLLL think the converse to Fermar's Little Theorem is true? 10.8 Theorem. Lern be a natural number greater than 1. Then 7 is prime if and only if a"- = 1 (mod n for all natural numbers a less than n. 10.9 Question. Does the previous theorem give a polynomial or exponen- rial time primalin test? Inventing polynomial time primality tests is quite a challenge. One way to salvage some good from Fermat's Little Theorem is to weaken...