If a and b are integers such that a? = b² (mod p), where p is prime integer, then a) a = b (mod p) b) a = -b (mod p) c) Both (a) and (b) d) Neither (a) nor (b)

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

A:

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: 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