Find a number a between 0 and 86 such that 71122 = a (mod 87).

Q: The number 73 is prime. Enter an a such that 0 <a < 73 and a = 6 (mod 73), if such an a exists.…

A:

Q: Find an integer x satisfying the equation: 4x21 = 2(mod 5) or show that no such integer exists.

A:

Q: Find the solution to 34x = 77(mod 89) that is positive and less than 89.

A: given that                                          34x≡77 (mod 89) we have to find positive…

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

A: Ans: -87

Q: Express each nonnegative integer a less than 15 as a pair (a mod 3, a mod 5).

A: The values of a could be, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: The notation x = y mod n is used to indicate the unique integer x in the range 0 :$ x &lt; n such…

A: Given statement is that the notation x = y mod n is used to indicate the unique integer x in the…

Q: Give an odd prime p congruent to ±1 modulo 12. Show that (3) = 1.

A: Please see the attachment

Q: Recall that 2027 is a prime number. Compute all values of x E {0, 1, 2, ..., 2026} such that 999x =…

A:

Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: Compute 2021^2021(mod 1000). The answer is 421. Show the work.

A:

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

A:

Q: Find all solutions in {0, 1,2, ..., 12} to x26 + 15x13 = 12 mod 13.

A:

Q: Find the primitive roots (mod 17).

A:

Q: a be an odd integer. Pro

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: Suppose that a is an odd integer and (a, 91) = 1. Prove that a12 ≡ 1 (mod 1456).

A:

Q: Find an integer a such that a 400 = 1(mod 3911).

A:

Q: 111111 is prime. Prove that, in any radix b, The number 11111 (11...1), can be prime only if the…

A: As per the question we have to prove that the number 111...1 containing n number of 1's will be…

Q: Determine a positive integer x such that 57x +7 = 78 (mod53).

A:

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

A:

Q: Suppose b is any integer. If  b mod 12 = 5,  what is 6b mod 12? In other words, if division of b by…

A:

Q: and 10 9. Use Euler's theorem to evaluate 2100000 (mod 77). An11

A:

Q: 23219 Compute 11 mod 3. Show your work and justify each step.

A:

Q: find the integer x such that 0 < x < 232 and 144x = 4(mod 233). Show your work.

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: 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: Find a number a such that 70a = 1 mod 17.

A:

Q: Find all x EZ221 such that x2 =97 (mod 221).

A: To find : all x∈ℤ221 such that x2≡97mod 221 Pre-requisite : Properties of Legendre symbol - 1. ap=1,…

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Find the smallest positive integer for which x mod 3=2 and x mod 4=3   What is the next smallest…

A:

Q: Number theory

A:

Q: Use Hensel Lifting (twice) to find a solution to x² = 7 (mod 374).

A: According to the given information, it is required to use Hensel lifting method to find the…

Q: Consider modulo 11. a. Find 35 mod(11). b. Find a negative integer x such that x mod(11) is…

A:

Q: (a) Let p be an odd prime. Give an analogue of the quadratic formula mod p, and prove it. (b)…

A: (a) Given that p is an odd prime.  The quadratic formula mod p is given by: ax2+bx+c≡0mod p Here, p…

Q: Suppose that a and b are integers, a = 4(mod 13), and b = 9(mod 13). Find the integer c with 0<c< 12…

A: We will use the basic properties of congruence modulo n relation to answer this question.

Q: For any integer a, a37 = ? mod 1729

A: Option b is correct answer

Q: 2. Find all solutions, or show there are none, to the congruence X78 = 5 (mod 19)

A: By Fermat little theorem x18≡1mod19. Therefore, x4×18+6≡x6mod19 or x78≡x6mod19.

Q: determine n between 0 and 16 such that (405)(777) is congruent n(mod 17)

A:

Q: 2. Find an inverse of 2 modulo 17 that is positive and less than 17.

A:

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

A:

Q: The order of 5 mod 17 is

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

Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: Consider numbers of the form 9" mod 13, where n E Z+. We claim that all of these numbers will only…

A: First principle of mathematical induction : Suppose Pn is a statement where n∈ℤ+ . The statement is…

Q: 4) The least positive integer residue of 21000000 mod 17 is a) - 1 b) 1 c) 2 d) a

A:

Q: 5. Find a number a such that 0<a<111 and (10270 + 1)38 = a (mod 111).

A:

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: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: Find all the integers that satisfy 140x = 133 (mod 301).

A:

Q: Find the smallest positive integer xx that solves the congruence: 11x≡5(mod57)

A:

Q: Find the least residue of 13^456 (mod 31)

A: Solution

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.