Find 28!mod 29. The answer should be an integer x where 0 < x < 28.

Q: The number 73 is prime. Enter an a such that 0 <a < 73 and a = 6 (mod 73), if such an a exists.…

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Q: For which odd primes p is 3 a square mod p?

A:

Q: Prove the following:For any natural number n, if n 2 + 6 n is an even number, then n is an even…

A: To prve that n is an even integer under the given conditions

Q: Find the answer of -16 mod 5

A:

Q: The integer n = 12700140x3243243 is missing the digit x. a) If n congruent to  3 (mod 9), then what…

A: According to the given information, Consider the given integer n:

Q: 2n-1 b) Prove that if , r #1 (mod 2"), then n is even.

A: Given that x2n-1≢1mod2n . The objective is to show that n is even. The x2n-1≢1mod2n can be written…

Q: Show that 2 is a primitive root modulo 3" for all n > 1.

A: To prove that 2 is a primitive root modulo 3n for all n≥1.

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: The square of an even integer is congruent to 0 (mod 4). Select one: O True O False

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

Q: Express each nonnegative integer a less than 15 as a pair (a mod 3, a mod 5).

A: The values of a could be, 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: Find a primitive root of 29 Solve x6 = 4 (mod 29)

A:

Q: Find the smallest integer a > 1 such that a –1 = 2a (mod 11

A: To find:

Q: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

Q: an is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod…

A:

Q: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.) O -11 4 6…

A: Which of these integers are in the congruence class of 11 mod 7? (Select all that apply.)

Q: For each nonnegative integer i, what is the least residue modulo 9 or 10i?

A:

Q: x is congruent to 43 mod 12. Then x is

A: x is congruent to 43 mod 12 implies x congruent 7 (mod 12). So, solution in the least residue system…

Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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Q: Let be a prime number. Stating any results that you use, deduce that xº-1 = (x – 1)(x – 2) · . · (x…

A:

Q: Where would 129 be on a mod 13 clock (which goes from 0 to 12)? What is the remainder…

A: Where  would  129  be  on  a  mod  13  clock  (which  goes  from 0 to 12)? What is the remainder…

Q: Given a = 4( mod 9) and b = 5( mod 9), find c with 0<c<9 such that c = 5a + 3b ( mod 9)

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Q: 5x = 7 (mod 32)

A: To solve the following problem

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

A: Linear congruence

Q: find the integer x such that 0 < x < 232 and 144x = 4(mod 233). Show your work.

A:

Q: Suppose that a ≡ 9(mod 13) and b ≡ 7(mod 13). Find the integer cwith0≤c≤12suchthatc≡2a2 −6b2(mod13).

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Q: X = 17 (mod 21) X= - ) 8 Cmod 25

A:

Q: Find a number a such that 70a = 1 mod 17.

A:

Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

Q: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: Use Hensel Lifting (twice) to find a solution to x² = 7 (mod 374).

A: According to the given information, it is required to use Hensel lifting method to find the…

Q: b) Determine whether or not x? = 85 (mod 97) has a solution.

A:

Q: he smallest positive integer x such that x = 22 (mod 25), x =

A:

Q: Suppose that a and b are integers, a = 4(mod 13), and b = 9(mod 13). Find the integer c with 0<c< 12…

A: We will use the basic properties of congruence modulo n relation to answer this question.

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: State whether True or False: If A and B are integers and A ≡ 3 (mod 3) and B ≡ 2 (mod 6) then A+B ≡…

A:

Q: 2. Find an inverse of 2 modulo 17 that is positive and less than 17.

A:

Q: (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

A: (d) For all integers a and b, if ab=7 mod 12, then either a =1 mod 12 or a =7 mod 12

Q: The number of incongruent primitive roots modulo a prime p is: a) Ø(p) b) Фф — 1) с) р—1 O a O b

A:

Q: (b) Let x be an integer such that 0 < x < 8 and (10500 + 105000 ) = x (mod 9). Justifying your…

A: We have to find the required value of x .

Q: Find the integer a such that a ≡ 71( mod 47) and -46  ≤ a ≤ 0  I need a better understanding of how…

A:

Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.

A:

Q: Write a formal proof for the following. For all integers a and b, if a ≡ 1 (mod 4) and b ≡ 3 (mod…

A:

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: "Given: x = -30 (mod 12) Which of the following integers are valid solutions for x 18- O 30 20 36-

A: Solution:- -30mod(12) To obtain -30mod12 conduct these three steps:

Q: Find all solutions of 3* = 17 (mod 224)

A:

Q: 2222 (mod 13) is equal to 12 (mod 13) 2 (mod 13) None of the mentioned 6 (mod 13) 1 (mod 13)

A:

Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: Find all the integers that satisfy 140x = 133 (mod 301).

A:

Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.