Find all solutions to the congruence5x−3 = 4 (mod 25). If none exists, explain why. If there are one or more solutions, give a complete list of solution(s)

Q: Let a be an integer such that a = 4 mod 12. Use the definition of mod to prove that a² = 4 mod 12-

A: Solution-:                           a≡4 mod 12a2=(4)2 mod 12     =16 mod  12     =4   mod   12

Q: For NP- Complete problem, the solution can be verified in polynomial time easily . True False

A: I have given an answer in step 2.

Q: Give a proof by cases that x ≤ |x| for all real numbers x.

A:

Q: Prove by Contradiction: For all integers x and y, x^2 - 4y is not equal to 2

A: Answer :

Q: Which option is correct for the following system equation? x-y-z=4 2x-2y-2z=8 5x - 5y - 5z = 20…

A: According to the Question below the Solution:

Q: Example 18 Solve the following system of congruence's by using Chinese Remainder Theorem x = 3 (mod…

A: X≡3(mod 7 )X≡5(mod 9 )X≡4(mod 5 ) Establish the basic notation. In this problem we have k=3 a1=3,…

Q: Consider that the given points are as follows:

A: As we have to use the curve fitting technique with the generic algorithm. Look at the given data…

Q: Please solve quickly with c++

A: Coded using C++.

Q: Solve for the root of a nonlinear equation when a = 2 and b= -1 using incremental search method on a…

A: Given: Solve for the root of a nonlinear equation when a = 2 and b= -1 using incremental search…

Q: (cos n) Find the limit of the sequence an 3n

A: Answer

Q: Graph f(x) = cos(?) − ?, 0 ≤ ? ≤ ?/2 and then use Solver to find the zero(s) of ?(?) correct up to…

A: Graph f(x) = cos(?) − ?, 0 ≤ ? ≤ ?/2 and then use Solver to find the zero(s) of ?(?) correct up to…

Q: А.В.С+А.B.C;

A: Simplified the given boolean function

Q: F. Find a root of an equation f(x) = x³ -x-1 using Bisection method. The = f(x) <0.

A:

Q: is ¬(p -> q) logically equivalent with p ^ ¬q? Show your solution.

A: We will prove it via the truth table and normal laws   Let us take ~(p -&gt; q) As per conditional…

Q: Prove that 2n = o(22n).

A:

Q: T(n) = 3T(n/2) + n

A: The given equation: T(n) = 3T(n/2) + n

Q: 50 to = 0, t1 = 1, tn = 6t,-1 – n. 9tn-2 +

A: The solution to the given question is:

Q: To solve x such that 29x = 1 mod 100, we need to find the inverse of x. For such an inverse to…

A: If two integers a and b are coprimes, then only positive integer that is a divisor of both of them…

Q: T(n) = 4T(n/2)+n/ log n

A: Master's theorem is given by if given equation is T(n) = a T(nb) + θ(nklogpn) a⩾1, b⩾1,k⩾0 and p is…

Q: Solve the recurrence: T(n) = 3T(4)+n* – lg n Use the master theorem to solve the following…

A: Given  Recurrence relation is  T(n) = 3T(3n/4) + n⁴ - log n

Q: T(n) = T(n/2) +n(2 – cos n)

A: Solution   Given Recurrence:                                  T(n) = T(n/2) + n(2 - cos n)

Q: SHOW YOUR SOLUTION  Find the exact running time T(n) then explain of how you solve or get the…

A: Question : What is the value of sum after the code below is executed?#include&lt;stdio.h&gt;int…

Q: Please solve quickly

A: Generalized pentagonal numbers and centered hexagonal numbers Generalized pentagonal numbers are…

Q: :) Form the interpolating polynomial of degree k that satisfies pG) (xo) = fG) (xo) for 0 <j< k.

A: Polynomial interpolation is a method of estimating values between known data points.

Q: Solve using Runge- Kutta Method of Order 4 For x, 0≤x≤ 2, Use h = 0.2 in dy dx (x + y) sin xy, y(0)…

A: Code:   h = 0.2; x = 0:h:2; y = zeros(1,length(x)); y(1) = 5; n = length(x)-1;…

Q: T'п) — ЗТ (п/3) + n/2

A: Solution   Given recurrence equation is,                                                  T(n) =…

Q: Prove that {02"|n 2 1 and n E N} is not regular using the Pumping Lemma

A: Here, I have to prove the given language is not regular using pumping lemma.

Q: Find the following sums of series. 10 F1 = > k? k=0

A: Iterate k from 0 to 10 and add k2 to f1 Thus, f1 will have summation of squares

Q: Give solution OOP C++

A: Object :  Real time entity  For instance if we consider the example of a set of fruits comprising of…

Q: If the TSP gives a solution x, checking whether the solution is correct or not, it takes a. None of…

A: 1.) The solution of the first question i.e. if TSP gives a solution x is " ( d.) exponential time".…

Q: Solve the following recurrence equation using the iterative Method, show the details of your…

A: We have to solve given recurrence relation using the iterative method.  In this, we will put n…

Q: Solve second part please

A:

Q: Write down the C++ code for Jacobi method to solve the following linear systems with .

A: required: Write down the C++ code for Jacobi method to solve the linear systems.   all the code…

Q: Determine the value of variable m with the determinant of the matrix N= 2, the matrix N is given as:

A: Let's first find the determinant of the given Matrix N Steps: N = m3 * ( (0 * 1) - (0 * 1) ) - m2…

Q: T(n) = 6T(n/3) +n² log n

A: Given question ::- 6T(n/3) + n2logn

Q: Find all solutions of the following congruence(s). Show all work. 2x ≡ 5 mod 7

A: As per policy we can answer only one question for answer of other question please ask separately

Q: If gcd(a, m) = 1, then the unique solution xo to ax = b (mod m) is equal to (1) xo = ab (mod m)

A: An inverse function is a function that reverse another function.

Q: Solve this with complete solution please

A: Summary: In this question, we have been given two decimal numbers and we have to change divide them…

Q: In a bisection method, after applying one iteration, by how much did our interval that might contain…

A: To find the % of interval that contain a zero of f(x) decrease  after applying one iteration in…

Q: Please solve Quickly

A: NOTE Below is the answer for the given question. Hope you understand it well. If you have any…

Q: 7. Find the remainder of when divided by a. 2. ь. 5. c. 7. d. 9. 8. Solve the following congruences…

A: Here is the detailed explanation of the solution.

Q: T(n) = 64T(n/8) – n² log n

A: Given equation ::-  T(n) = 64T(n/8) - n2logn.

Q: Prove that if a and b are positive integers such that a|b and b|a, then a = b USE ANY METHOD

A: Given:  Prove that if a and b are positive integers such that a|b and b|a, then a = b USE ANY METHOD

Q: T(п) — /2) + п" 2"T(n, n

A: The given equation :-  T(n) = 2nT(n/2) + nn

Q: please solve for  (a) (b) (c)

A: Please give positive ratings for my efforts. Thanks.   ANSWER

Q: QUESTION 3 Find k, if any, such that AB= BA where 2 5 4 -5 A = and B=

A: Value of k , if AB=BA

Q: Consider the following adigorifhms which apprOximate the solution y 1,2, ... at every iteration. by…

A: The idea of the fixed point iteration methods is to first reformulate a equation to an equivalent…

Q: Do 2-iterations of the Secant method for finding a root of the equation f(x)=cos(x)-x*e^x=O start…

A: Summary : the root is 0.83853

Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.