a) Find all solutions to the congruence 10r = 5 mod 15

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: Use this theorem to solve the following congruences: x1 = 13 mod 35

A:

Q: Problem 3. Solve the linear congruence 7x = 13 (mod 19).

A:

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).

A:

Q: 1- Determine the number of solutions of the congruence   x4≡ 61 (mod 117). PLZ WITH DETAILS.

A: Given: x4≡61(mod117) 117=32×13 As ϕ(9)4,ϕ(9)=64,6=62=3                  (here 4,6 denotes the g.c.d…

Q: 1. Solve the following linear congruence using a systematic method: 167x = 241 (mod 199) Present…

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

A:

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

A:

Q: x43 = 47 (mod 713)

A: Step:-1 By Chinese remainder Theorem (CRT),  x43 ≡ 47 mod 713 if and only if x43 ≡47 mod 23 ⇒x43 ≡1…

Q: Solve the linear congruence 10x ≡ 15 (mod 45).

A:

Q: 1. Find all simultaneous solutions of the congruences: (a) X= 3 mod 5 x= 4 mod 6

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Q: solve the following linear congruence : 17x congruence 3 (mod 7)

A: Consider the provided question,

Q: Solve the following linear congruence: 25x = 15 (mod 29).

A:

Q: 5x = 7 (mod 32)

A: To solve the following problem

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: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: Solve the following linear congruence 6x ≡15 (mod 21)

A:

Q: Solve the congruence: 341x + 19 = 291 (mod 9).

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Q: Solve the following linear congruence: 36x = 8 (mod 102).

A: The linear congruence ax ≅b(mod m) has a solution iff d|b where d=(a, m)

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: Find all incongruent solutions - if exist - for the congruence: 36x = 96 mod 156

A:

Q: Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x' = 13 mod 35

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

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: Write the set of solutions of x=5 (mod 24) x= 17 (mod 18), if any as the solutions to a single…

A: We have a set of congruence as x ≡ 5 (mod 24)x ≡ 17 (mod 18) From the first equation we can write…

Q: #5. Find all incongruent solutions of each quadratic congruence below. (a) x? = 23 mod 77 (Hint:…

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Q: Solve the following linear congruence: 25x = 15 (mod 29). استعراض مركز ملفات المحتوى هاز الكومبيوتر

A:

Q: #5. Find all incongruent solutions of each quadratic congruence below. (a) x? = 23 mod 77 (Hint:…

A:

Q: he solution of the linear congruence 103x = 444 (mod 999) is ) 111 ) 222 2 333 ) 444

A: We have to find x such that  103x = 444(mod 999)

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: 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: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: Question 2 Solve the linear congruence 19x =7 (mod 90127)

A: We have to Solve given linear congruence by following way.

Q: Solve the following congruence equations. 1. x=2 mod 3 2. 9x = 21 mod 30 3. 18x = 30 mod 42

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Solve the following linear congruence. 36x = 8 (mod 102).

A: On solving ,we get

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

A: The given congruence equation is                                             3x+12≡7 mod 10

Q: 3

A:

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 congruence 2² +1 =0 mod 133.

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Q: Find all solutions in {0,1,...,43} to 6x=10 mod 44

A: In general,  ax ≡ b (mod m) has solution if gcd(a,m) divides b    If gcd(a,m) = 1 then solution is…

Q: solution to the congruence equation (3x + 12) = 7 mod 10

A: Given :  3x+12=7mod 10⇒     3x=7-12 mod 10⇒     3x=-5 mod 10⇒     3x=5 mod 10        -5 mod 10 =5⇒…

Q: Find all whole number solutions of the congruence equation. 4x+6 ≡ 5 mod 8

A:

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

A:

Q: solve the following congruence equation:3x+58 ≡1(mod 12)

A: If ab≡bc(mod nb) then a≡c(mod n) And if ab≡bc(mod n) and if (b,n)=1 then a≡c(mod n)

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.