Consider the linear congruence 15 = 1113 (mod 10371). If given that gcd(15, 10371) = 3, then answer the following questions. (a) How many solutions does the congruence have? (b) Simplify the congruence. Show your work. (c) Find a solution to the simplified congruence you found in (b). Show ur steps. (d) Find the first two solutions.

Q: (a) Solve the linear congruence 26x = 1 modulo 33

A: Solution

Q: Consider the linear congruence 27 = 105 (mod 4965). If given that gcd(27, 4965) = 3, then answer the…

A: Notes: the variable x is missing in the question. I had rectified in my solution.

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

A:

Q: Solve for : y = 14x + 4 (mod 51) Step 1. subtract 4 y- 4 154 Step 2. Find the multiplicative inverse…

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Q: Fill in the following blanks. Suppose you are finding 15^-1 (mod 131). This problem is equivalent to…

A: Answer follows

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Q: 2.23 Find all four solutions to the equation x²10 (mod 35).

A: The given equation is: x2-1≡0 mod 35 We have to find all four solutions to the given equation.

Q: Find the smallest positive integer solution to the following linear congruence: 7r 13 (mod 34).

A:

Q: Find a primitive third root of unity e F7, then verify by direct computation that (5 - 5)? = -3 in…

A: Primitive roots are those x which satisfy x^k = 1 mod n

Q: Find the solutions of a3 – 24.x2 + 54 = 0( mod 25).

A: want to find solution of x3-24x2+54≡0(mod 25)note that1 a≡b(mod m) f and only if m|a-b(i.e a-b=mk…

Q: (a) Solve for x if 25x = 15(mod 29).

A: Linear congruence

Q: Bruce and Cruz had 294 bookmarks altogether. Bruce gave away 3/8 of his bookmarks and Cruz gave away…

A: Let the number of bookmarks Bruce has = B The number of bookmarks Cruz has = C therefore B+C=294…

Q: (2) (a) Find all of the solutions modulo 15 to 6x = 15 mod 18. Express your answer in terms of the…

A: Given, 6x≡15 mod 18. As it is known that, an≡bn mod cn ⇔ a≡b mod c. Therefore, we have 6x≡15 mod 18…

Q: For each of the following equations determine if they have a solution. If yes, find the solutions,…

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Q: D. Determine the number of incongruent solutions of each linear congruence. 1. 22x = 18 (mod 75)…

A: Given linear congruence is  1. 22x≡18mod 752.   2z≡119mod 983.   9x≡95mod 36

Q: (a) Find all solutions r to the congruence 341x = 16 mod 912

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (3) Solve the system of congruences: I = 2 mod 5 I = 3 mod 8 I = 7 mod 11

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Q: x = 10 (mod 18), x = 14 (mod w). Solve system of congruences, find the smallest possible value for…

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Q: 3. Use congruences to prove the following: (a) 4"-1 is divisible by 3 for every natural number n.…

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Q: Consider the linear congruence 22 = 712 (mod 4366). If given that gcd(22, 4366) = 2, then answer the…

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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: y²=x³-5x+3 (mod5). solve for all x and y, when x is at least 0, and y is at most 4

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Q: 5. Solve the following quadratic congruence using the "completing the square" method: 9x² +66x +49 =…

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Q: k from problem 2 and the method used in the example at the end of solve the congruence: 7x³ = 6…

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Q: Which table is a probability distribution table? X 1 P 0.4 X 1 P 0.4 X 1 P-0.2 X 1 P 0.2 2 0.15 2…

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Q: How do I use the Chinese Remainder Thm to solve this system of congrunces below? x ≡ 1 (mod 3) x ≡ 4…

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

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Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

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Q: Find a Diophantine equation equivalent to 3x = 5 (mod 11) and use the solution of the Diophantine…

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Q: Consider the linear congruence 22 = 712 (mod 4366). If given that ged(22, 4366) = 2, then answer the…

A: consider the linear congruence 22≡712mod 4366 given that gcd22, 4366=2 (a) how many solutions does…

Q: Using course notes, solve the congruence x³ + 3x² - 4 = 0(mod11²3²)

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Q: find the congruence for the following congruence equations: (1) 18x=3 (mod47)

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Q: a. Find the inverse of 43 (mod 256) b. Solve the linear congruence 43x=7(mod 256)

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Q: Find all solutions of the following linear congruences, Inverses (when required) may not be…

A: Given: 14x≡6(mod 31) Here a=14; b=6 and N=31 Also gcd(14,31)=1 Hence there can be only one value of…