11) The solution of the linear congruences x = 1 (mod 2), x = 2 (mod 3), x = 3 (mod 5), x = 4 (mod 7), x = 5 (mod 11) is: a) 1253 b) 1235 c) 1532 d) 1523

Q: Explain why F, contains a primitive nth root of unity if and only if p = 1 mod n. Hint : Use the…

A: To prove  Fp contains a primitive nth root of unity if and only if p≡1mod n (or n divides p-1).

Q: Fine GCD a-(18,45) b-(25,125)

A:

Q: Expand 2) 2m²k4

A: Topic-Exponents

Q: Prove that if a, b e R, then (a) -(a+b) = (-a) + (-b), (b) (-a)·(-b) = a · b,

A: (a) Proof of the fact -(a+b)=(-a)+(-b): Since -1 is additive inverse of 1, hence  −1+1=0   (zero in…

Q: Proficiency #9. [Modular Arithmetic] Prove that 13,050,046 is not the square of a natural number.

A: Solution: Consider the given number is : a = 13,050,046 We know that All perfect squares end in 1,…

Q: example of a real number greater than 0

A: All the positive , negative , rational , irrational numbers are called the real numbers. It can also…

Q: Every natural number greater than 1 can be written as the products of prime numbers.

A: Prove that  every natural number greater than 1 can be expressed as product of primes or the number…

Q: čc-8th-numbers-operations/cc-8th-exponent-properties/e/powers-of-prc Select the equivalent…

A: To find (x^4.y^4)^3

Q: (72) (9a3)

A: Given that : The expression is ( 7 x5 )( 9x3 ).

Q: Rewrite as a power of æ. What is the exponent on the æ?

A: The expression is x8x-2.

Q: Prove that if æ is a real number, then [2a] = [x] +

A: If x is a real number then  to prove- 2x=x+x+12 Greatest integer function is denoted by [x] for any…

Q: Color Volume (liters) Scientific Notation Purple 0.000125 1.25 10-4. Red 0.0002 2 x 10-4. Blue 325…

A:

Q: (3-V2x)(3 + V2x

A: Formula to be used : (a - b)(a + b) = a² - b²   Put, a = 3 & b = √(2x)

Q: Every natural number can be written as the products of prime numbers

A: Every natural number can be written as product of prime number

Q: direct proof: prove the following  Claim: The sum of two even integers equals an even integer…

A:

Q: Discrete Math Let a be an odd integer. Show that (a) 8 | a^2 − 9; (b) 16 | a^4 − 81.

A:

Q: 2 facts about laws for zero and negative exponents 3 insights about zero and negative exponents and…

A: Answer:          Zero exponents:                                     It's an exponent that always…

Q: All Fermat's number is clearly odd numbers

A: Fermat number.

Q: Using laws of exponents, simplify and then evaluate: 1. (3^3*3)^2+[(2)^5/(-2)^2]^3 2.…

A: Using laws of exponents, we have to simplify and then we have to evaluate: 1.…

Q: Using calculus, find two non-negative real numbers whose sum is 8 and have the smallest possible…

A: The objective is to find two non-negative real numbers whose sum is 8 and have the smallest possible…

Q: A value of a number in any base can be expressed as a polynomial expression using expansion method

A: Polynomials are the number in base x A number is defined as the sum of all the digits multiplied by…

Q: Laws of Exponent and its definition

A: Since laws of exponent and important laws of exponent

Q: 1. The value of the 5 in the number 594,631 is how many times larger than the value of the 5 in the…

A: Given: The first number  = 594,631 The second number = 859,463