Using Fermat's Little Theorem find 52003 mod 455. Note that 455 is not a prime number and 455 5*7*13.

Q: 4965 4 mod 5 4965 = 2 mod 7 4965 = 1 mod 11 Use your answers above to find the canonical…

A:

Q: The prime number 8191 is a None Inverse of 7 modulo 11 Carmichael umber Mersenne prime mmber

A:

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: Prove 10^47+67 is not a prime(use Fermat's). Thank you :)

A:

Q: 4. Find all numbers between -50 and 50 which x mod 13 = 3

A:

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: The square of an even integer is congruent to 0 (mod 4). Select one: O True O False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Eulers thm to find , 7଼8003 mod 1000

A:

Q: Congruence conditions (mod 20) for primes p for which -5 is a square (mod p).

A:

Q: an is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod…

A:

Q: Any two integers are congruent modulo .. when they are both even or both odd. Least common multiple…

A: Given a statement

Q: a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove…

A: Want to prove:(a) 10n≡±1 (mod 11) for any n∈N(b) If the integer x has digits xnxn-1.....x1x0 thenx≡0…

Q: Let be a prime number. Stating any results that you use, deduce that xº-1 = (x – 1)(x – 2) · . · (x…

A:

Q: For which primes p > 5 is -5 a square mod p? Your answer should be of the formp = {a1, a2, ..., ak}…

A:

Q: Where would 129 be on a mod 13 clock (which goes from 0 to 12)? What is the remainder…

A: Where  would  129  be  on  a  mod  13  clock  (which  goes  from 0 to 12)? What is the remainder…

Q: which of the below integers is congruent to 6 modulo 12 O 40 O 34 O 30 O none

A:

Q: Show that every nonzero residue (mod 17) can be written as a power of 3

A:

Q: 10. Find the value of 5368 (mod 41) Answer: Show your work here:

A: To find the value of- 5368(mod41)

Q: Suppose n > 1 is a composite integer ab where a and b are unequal integers both greater than 1.…

A:

Q: 5. Use the method of successive squaring to compute 3875 (mod 103) 1

A:

Q: What prime numbers are squares in mod 17? (Include primes that are larger than 17). What primes p…

A: Since the squares less than 17 are 1, 4, 9, 16 then the prime numbers that are squares in mod 17 are…

Q: Suppose that residue(modp) 8) Let odd prime P. atzis Show that has be an not Diophantine…

A: Given that a is not a quadratic residue mod p. That is there does not exists an integer z such that,…

Q: The prime number 8191 is a None Mersenne prime number Carmichael number Inverse of 7 modulo 11

A: Given that The prime number 8191 is

Q: 8. Use Euler's Theorem to find a number a between 0 and 9 such that a is congruent to 7 1000 modulo…

A: We know according to  Euler's Theorem  that  xϕ(n)≡1(mod n) where the function ϕ(n) counts the…

Q: 2

A:

Q: Use Fermat's Little Theorem to find (Show work.) a) 945 mod.23. b) 231002 mod. 41 c) (-9)933 mod. 13

A: Fermat's Little theorem states that " if p is a prime number and a is not divisible by p then…

Q: Determine what number the product is congruent to in mod 3. 5.8 5.8 = (mod 3 )

A:

Q: Characterize the primes p mod 20 such ial

A: We have to characterize p mod 20 such that -5p=1.

Q: Suppose that p is a prime number. Given this information prove that if x is an integer such that x^2…

A:

Q: Find an integer A so that: A79 = 7 (mod 277) Please solve step by step thanks!

A: Given an equation. Let's solve for A.

Q: 10. Use Euler's Theorem to show that 516) = 1 (mod 16).

A: Euler's theorem states that          "If gcd(a, n) = 1, then aφ(n) = 1 (mod n)

Q: Euler's Theorem states that if n is a positive integer and a is relatively prime to n, then ar(n) =…

A:

Q: Given any odd prime p, prove that: 2(p−3)! ≡−1 mod p. (Hint: Start with 2(p−3)!≡x mod p. Then work…

A: Let p be any odd prime number.  So we start with  2p-3!≡x mod p Also we have p-2≡-2 mod pp-1≡-1 mod…

Q: 122 is congruent to 5 modulo17 ?

A: To check whether -122 is congruent to 5 modulo 17 or not

Q: 100 nd a number between 0 and 12 that is congruent to 2"modulo 13. Show your work.

A:

Q: Show that if p and q are distinct primes, then pª-1 + q®=1 = 1 (mod pq).

A: Given problem is to show the following identity using congruence, we have to consider that…

Q: Find oll integers Such thot 24! x =1 Cmod 2) 5x = 3. (mod 8) and 1500 < X <2000

A:

Q: The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a…

A: Given:          a≡2 mod(7)  and b≡5 mod(7)

Q: The preceding part of the problem proves the reverse implication unless n = p2 where p is a prime.…

A:

Q: Using Fermat's theorem, find 3201 mod 11.

A: Euler's Theorem states that for any natural  number n, we  have  aϕ(n)≡1(mod n) where ϕ(n) denotes…

Q: Use Fermat's theorem, show that if ged(a, 155) 1 then a1 = a (mod 15

A:

Q: a) Use Fermat’s little theorem to compute 3302 mod 5, 3302 mod 7, and 3302 mod 11.b) Use your…

A:

Q: State Fermat's Little Theorem. In the groun (7/1017)x find 5100 5101 and 5202 (101 is a prime…

A:

Q: 8. Show that 18!= -1 (mod 437). 9. Using Euler's Theorem, find the last two digits of 44443333 10.…

A:

Q: Use Euler's theorem to evaluate: 9 (mod 14) for a =1446.

A: Euler's theorem:- If gcd a,n=1 then aϕn≡1mod n. here ϕn is Euler's function. The number of integer…

Q: mod 32, given Xo=1 Please answer w

A: The congruential generator is given as:Xi+1 = 11Xi mod 32, where we are given X0 = 1. We see that,…

Q: 3x is congruent to 2 mod 13

A:

Q: 2222 (mod 13) is equal to 12 (mod 13) 2 (mod 13) None of the mentioned 6 (mod 13) 1 (mod 13)

A:

Q: Fermat's Little Theorem tells us that if p is prime and a is an integer not divisible by p, then…

A: