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

Q: Solve the following congruences: (a) 3x  8 (mod 5) (b) 3x  8 (mod 12)

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Q: 5. 2x 15 (mod 17) 6. 4x 6 (mod 17)

A: According to our guidelines we can do at most three subpart of a question at a time. So please post…

Q: Solve the quadratic congruence, 6x²-7x+2 ≡ 0 mod 31.

A: We have to solve the above quadratic congurence.

Q: Q2: Find the solution of 143x³ + 22x¹ + 5x² + 3x + 1 = 0 (mod 11), if any.

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Q: Solve the following system 3x + 5y − 7z ≡ 8 (mod 83) 8x − 9y + 13z ≡ 13 (mod 83) 7x + 4y + 5z ≡ 15…

A: Let AX=B where, A=35-78-913745, X=xyz, B=81315 Therefore, we have: AA-1·X=A-1B           IX=A-1B…

Q: 7x = 4 (mod 12).

A:

Q: 4x=22(mod10)

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Q: 3x = 1 (mod 6)

A: 3x≡1 (mod 6) ⇒ 3x-1≡0 (mod 6)This means 3x-1 is divisible by 6.

Q: Solve the congruence 863x ≡ 880 (mod 2151).

A: we can observe that  863 and 2151 are co primes ,  that means  863 , 2151  = 1 and  1 / ( - 880 )…

Q: Determines the result of the following operations: a (7x5) (mod 6) ь. (9х 3) (mod 4) C. (12 x 11)…

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

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

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: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

Q: Find all the solutions to the linear congruences  (b) 128x = 833 mod 1001 (c) 36x = 30 mod 42

A:

Q: 5x² + 3x = 3(mod17) X = (mod17)

A: Given that 5x2+3x≡3 (mod 17)x(5x+3)≡3 (mod 17)x≡3 (mod 17)  or   (5x+3)≡3 (mod 17)x≡3 (mod 17)  or…

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

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Q: Find all solutions for 10x = 14 mod 1008

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Q: Solve the system 2.x = 3(mod 5) 3r 2(mod 7) I = 2(mod 6)

A: As per our guidelines we supposed to solve the very first question when multiple questions are…

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

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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: 2x² + 3x = 14(mod19) X = * (mod19)

A: Given,            2x2+3x≡14 (mod 19).

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: 5^14 ( mod 26).

A:

Q: Which of the following is false? a. (x-y+2) = (x-y-11) (mod13) b. (x-y+2) = (x-y-32) (mod 17) c.…

A: Sol:- Check each statement:- a.x-y+2≅x-y-11mod 13Since, 2 mod 13 = -11 , This statement is…

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

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Q: True or False. Briefly explain why.  The linear congruence 35x  ≡  5 mod 150 has 5 incongruent…

A: Given statement is,  The linear congruence 35x  ≡  5 mod 150 has 5 incongruent solutions modulo 150.…

Q: Solve the following equations in Z, giving full details of your analysis (a) 5x + 3 = 1 (mod 6) (b)…

A: We have to solve the equation in

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

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