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

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 all the solutions of the congruence equation x6-2x5= 35 (mod 6125).

A: Consider the given congruence equation. x6-2x5≡35mod 6125. Now, the prime factorization of 6125 is:…

Q: Solve a congruence equation and give all the solutions: 3(x – 2) + 4x = 5x +8 (mod 31)

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Q: 1. Find all solutions (a) 2x + 3 = 7 (b) 2x + 3 = 7 to the following congruences.. (mod 9) (mod 20)

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Q: 4. Solve each of these congruences using the modular inverses found in the previous problem. (a) 7x…

A: The given congruence equations are (a)    7x=2 (mod 26) (b)   19x=4  (mod 141)

Q: 2r = 3 4x = 2 3x 2 (mod 5) (mod 6) (mod 7).

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Q: 4. Solve the following quadratic congruences: 5x² + 6x + 1 = 0 (mod 23)

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

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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 system of congruences 2x ≡ 1 (mod 5) 3x ≡ 9 (mod 6) 4x ≡ 1 (mod 7) 5x ≡ 9 (mod 11) Hint:…

A: We can solve this system of congruences using the Chinese Remainder Theorem. First, let's write each…

Q: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: Which of the following linear congruence has 2 incongruent solutions? (a) 3x = 9 (mod21) (b) 14x =…

A: to solve linear congurence , ax≡b(mod m) .........(1) the first stem is to reduce the congurence  by…

Q: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: Does x2 +3x+7=0 mod 31 have solutions? IF

A: This follows in the same way as we study quadratic equations. Here we use facts about quadratic…

Q: Solve the following quadratic congruences: (a) 3x² + 9x + 7 = 0 (mod 13) (b) 5x² + 6x + 1 = 0 (mod…

A: According to Q&A guidelines, I can answer only one question. So I answered (a).

Q: Determine the system of linear congruences which yeild all the square roots of 31 modulo 33.

A: Please find the answer in next step

Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

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Q: solve the congruence of  6x=4 mod 10  aolve the conguence of 341x=2941 mod 9

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

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Solve the following linear congruences (you may if you wish, find some solutions by inspection): (a)…

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Q: (a) 64x 56 (mod 52) (b) 14x = 35 (mod 56)

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Q: 6. Find all incongruent solutions to each congruence. Show your steps. (a) 135x = 108 (mod 612) (b)…

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Q: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: Find the solution of the following equations: 6x = 1(mod 33), 7x 1(mod 9)

A: If the given congruence equation is:.It is known that if a and m are relatively prime, then the…

Q: 3. Solve the following congruences. † (a) 10x = 5 (mod 21) (b) 10x = 5 (mod 15) † (c) 10x = 4 (mod…

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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: Demonstrate that the equation x10 + y10 - z10 = 5 has no integer solution. (work with modulo 11)

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Q: Solve the quadratic congruence x² = 35 (mod 817).

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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: 2) Solve the following linear congruences: 14x = 91 (mod 189) 24x = 56 (mod 88)

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Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

Q: Solve the congruences: 52x + 4 = 8(mod 22) 17x = 19(mod 100) 3x = 9(mod 12)

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Q: 9. Find all the solutions of 3x² + 2x + 1 8 (mod 63).

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Q: olve the congruence8x= 16 (mod 424).  If none exists, explain why.  If there are one or…

A: The given equation is: 8x≡16mod 424

Q: Why does the linear congruence 25x ≡ 30 (mod 75) have no solutions?

A: To show that the linear congruence 25x≡30mod 75 have no solutions.

Q: Given that 3599 = 59-61, determine whether x² = 581 (mod 3599) has solutions.

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Q: where every entry on the diagonal of the matrix in the last line is 11, and every entry below the…

A: We have to find the values of a,b,c, and d.

Q: Find the whole number of (3+12) =7 mod 10

A: The given equation (3x+12) ≡7 mod 10. Consider the following congruence equation (3x+12) ≡7 mod 10.…

Q: 2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)

A: