Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: Find the answer of -16 mod 5

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Q: The equation 20x=30 (mod 70) has: 10 non-congruent solutions modulo 70 None of these no solution…

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Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 4. 8.

A: The given question is solved below.

Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: (3). (a). Find all solutions to the congruence 6x = 9 (mod 45)

A: To Determine :-  All solutions to the congruence : 6x ≡ 9   mod 45 .

Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

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Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

Q: Find all whole number solutions of the congruence equation.  2x+3 ≡ 8 mod 12

A: # we are entitled to solve one question at a time . Please resubmit the other question if you wish…

Q: Solve the linear congruence 2370x ≡ 69 (mod 2517) or say why no solutions exist

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

A: 7x≡5 (mod52)---(1)

Q: Find all solutions for the following pair of simultaneous congruences. 262x = 3 mod 807 3x = 2 mod 5

A: Given: The congruences, 262x≡3 mod 8073x ≡ 2 mod 5 To find: All solutions for the given pair of…

Q: Find the common solutions to the congruences 2x 3x 1 (mod 5) (mod 6) 1 (mod 7). 9 4x

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences.

Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101 We need to solve x2≡186 mod 101 and how many solution exists.

Q: Solve the congruence17x−3 = 4 (mod 26).

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Q: а). Solve the linear congruence of 231x = 147 mod 598 .

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Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

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Q: Solve the givnen congruence x2 ≡ 9 (mod 600).

A: The given problem is to solve the given congruence equation. x2=9 (mod 600).

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: The liñear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

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Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 16).

A: Congruence modulo relation on integers:Let a,b∈Z and let m be a fixed positive integer. Then we say…

Q: Use the index system modulo 19 to find all solutions of x3≡11(mod 19) and 5x≡4(mod 19).

A: The congruences given are as follows: x3≡11mod 195x≡4mod 19 We are asked to find the value of x that…

Q: x3-3x2+27 is congruent to 0 (mod 225)

A: Consider the following problem  x3-3x2+27≡0mod 225 Prime factorization of 225 is 32×52 Now,…

Q: Find all solutions mod 31 to the congruence z = -5 (mod 31).

A: We will use python code to find the solutions Now x5 ≡  -5 (mod 31)  ≡  26  (mod 31) And we only…

Q: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

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Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

A: We  will solve it by Chinese Remainder Theorem Given  x≡1(mod3)x≡2(mod4)x≡3(mod5) Compare it with…

Q: Solve the congruence x² = 79 mod91.

A: The given problem is to solve the given quadratic congruence equation. Given congruence x2=79(mod…

Q: Solve the congruence: 341x ≡ 2941 (mod 9).

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Q: Find all whole number solutions of the congruence equation. (2x + 1) ≡ 5 mod 4

A: Consider the given congruence equation. (2x + 1) ≡ 5 mod 4

Q: The equation 21x=49 (mod 70) has: * O None of these O no solution modulo 70 6 non-congruent…

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Q: Give all the integer solutions of the congruence 56x-12=0 (mod 23).

A: Given congruence 56x-12 ≡ 0 (mod 23) i.e., 56x ≡ 12 (mod 23) i.e., 10x ≡ 12 (mod 23) We know that,…

Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

Q: Use your work from problem 2 and the method used in the example at the end of Lecture 16 to solve…

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Q: The equation 12x=24 (mod 48) has: * no solution modulo 48 24 non-congruent solutions modulo 48 None…

A: Given the equation 12x≡24(mod 48)

Q: Find all solutions of x = 10 (mod 133).

A: A congruence of the form, f(x)≡0(modm), where f(x)=anxn+an-1xn-1+...+a1x+a0, ai=0,1,2,...,n is…

Q: Give all non-negative solutions for 10r =-17 mod 4.

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Q: Find all solutions of the congruence x2 ≡ 16 (mod 105).

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Q: Solve the congruence 9x   21 (mod 33).

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Q: Find all solutions to the congruence13x−3 = 4 (mod 26). If none exists, explain why.Your…

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Q: Find all the whole number solutions of the congruence equation. 3x 8 ≡ mod 11 3x + 12 ≡ 7 mod 10

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Q: 3

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Q: 3. Find all solutions of the congruence: 19x = 7 mod 69 .Show all steps to get full credits.

A: To find the solution of given linear congruence.

Q: 4. Solve the congruence 34x = 77 (mod 89).

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Q: Solve the linear congruence 5x = 3 (mod. 11). (Show all the work.)

A: The expression, a≡b (mod c)  implies that c divides a-b, that is when c divides a-b the remainder is…

Q: Number theory

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Q: Find all solutions mod 31 to the congruence x° = -5 (mod 31).

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Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 11 non-congruent solutions modulo…

A: Here we have given equation,  21x = 49 (mod 77)    Let a, b and m be integers such that m>0 and…

Q: Find all whole number solutions of the congruence equation. 3x+1≡ 4 mod 9

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Q: 4. Solve the congruence 34.x = 77 (mod 89).

A: in first process firstly we need to find the inverse to solve this type of question

Q: Solve the congruences. a) 5x =7 (mod 8) b) 11x 2 (mod 6)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.