10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

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

A: The given question is solved below.

Q: 7) Note that -2 is a square modulo 11. Indeed, 82 +2 = 6.11. Use this information, and the method of…

A: To use method of descent to construct a solution of x2+2y2=11 Now, it is known that -2 is a square…

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Q: (2) Prove by contradiction that if 3z2- is irrational then r is irrational. 215

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Q: For which integers c, 0<c < 30, does the congruence 12x == c (mod 30) have solutions? When there are…

A: Given congruence is 12x≡c(mod 30). We know that ax ≡b(mod m) have solutions when gcd(a,m) divides b.…

Q: 8. How many positive integers less than 1000 a) have exactly three decimal digits? b) have an odd…

A: According to our guideliness we can answer only the first 3 subparts. Positive integers less than…

Q: 15 Apply Garass elimination methad to solve the Sy stem, 2X+y+22=3, 3x -Y+ 4Z=7 4X +3y +6 2- S

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Q: , 7/4 /213, 33 b) Solve e In(9) + 21 = 41 for æ. a) Write In(- -) in the form a lIn(7) + bln(3)…

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Q: Consider the following IVP: у зу -10у - 1, уo) --1, у(0) - 2 Find the general solution. A 13 St re…

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Q: 2,2 and write tte answers in the comepute form of atib s 2.

A: Since you have posted a question with multiple sub parts we will solve first three sub parts for…

Q: 1. If today is Saturday, what day of the week will it be 1,500 days from today? 2. Prove that 4/2 +…

A: The explanation of the solution as follows:

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

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Q: The system 2x + 3y = 4 (mod 4) 3x + 4y = 5 (mod 4) has no solution modulo 4. Select one: True False

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Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: 4. Prove by contradiction: VmeZ, 7m+4 is not divisible by 7

A: Contrary suppose that,   m is an integer such that 7 m+4 is divisible by 7. By using the definition…

Q: Find all the non-congruent solutions to  4x ≡ 6(mod 21)  express solutions using the stand…

A: Introduction: A linear congruence is generalized as ax≡bmod n. The greatest common divisor of a and…

Q: Find the solution to an = 5an-2 — 4а, 4 with ao 3, aj = 2, a2 =6, and az = 8. Find the solution to…

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Q: The system x E 3 mod 9, x E 2 mod 4, has O A. no solution. O B. Unique solution. O C. finitely many…

A: Introduction: The Chinese remainder theorem is very significant in solving a system of linear…

Q: 3. (a) How many solutions are there of the equation x + y + z + t = 14, where x,y,z,t are…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

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Q: Q2.2 Compute 3 -7 2 3 3 -3 det 3 -8 2 - 3 2 2 (Entor the

A: according to the guidelines we should able to do only one question at a time #2.2

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 1. 4 2) 8)

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Q: 2. Prove by principle of Mathematical Induchion 6.7h - 2.3n is divisible by 4 for all nE 2#. 1

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

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Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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Q: 7. What necessary and sufficient condition do you need to impose on an integer c so that the…

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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: is a1 = 2, a2 =3, and an  = 5an–1 – 4an–2 for n > 2 expressed in explicit formula? true or false?

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Q: Prove that (-1+ iB)" + (-1- i3)" has either the velue 2t! or the value if a B any integer (positive,…

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Q: Explain why the congruence r2 = 2 (mod 4) has no solutions in Z

A: Result: Square of all integers modulo 4 is either 0 or 1.…

Q: Number Theory

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Q: Suppose ỹ = cje (:)- + czetx () is the general solution to = Aj. What is A O We don't have enough…

A: Use given differential equation y' = A y to find it.

Q: 7. How many integer solutions are there to 2r, + 2tz + 2rz + Xg +X5 = 9 with x; 2 0? (Hint: break…

A: Solutions to the equation are the set of values for which equations returns the same value on both…

Q: 19, Obtain the eight incongruent solutions of the linear congruence 3x + 4y = 5 (moi 84 ELEMENTARY…

A: To obtain the eight incongruent solutions of the linear congruence.

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 2) 8. 4

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Q: ulus) 1) Solve the following congruences system. 5x +4 = 12 (Mod 7) 14x - 3 = 19 (Mod 5) 2) Prove…

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Q: 9. One merchant has seven Asava horses (A), a second has nine Haya horses (H), and a third has ten…

A: Given, One Merchant has seven Asava horses (A), a second has nine Haya horses (H) and third has ten…

Q: Prove they are equal 4 = 7(2x+ 1) - 5x -3(3x + 1)

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Q: 5 - compute – 5A 3 Given A 3

A: we have to calculate -5A

Q: Number theory

A: Assume a=x2

Q: How do I use the Chinese Remainder Thm. to solve this system of congruences?? x ≡ 2 (mod 3) x ≡ 6…

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Q: B. Solve the system of congruence's x = 5 (mod 2), x= 7 (mod 5), x= 3 (mod 7)

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Q: Which of the following is the solution set of In(5x – 7) < In(2x + 8) (5, 00) (-00, 5] (-00, 5) [5,…

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Q: How many non-negative integer solutions are there for the following equation such that 0 < x1 < 10?…

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Q: Solve the system of congruence x ≡ 3 (mod 6) and x ≡ 4 (mod 7) using the method of back…

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