For p = 5 , find a number x such that x^2 is congurent to -1...

For p = 5 , find a number x such that x^2 is congurent to -1 mod p. here x is denoted by sqrt(-1). Determine if sqrt(-1) exists mod p for p = 7, 11, 13 , 17, 23, 29.

Expert Solution

This Problem has been solved using congruences in Zp.

Colby Messinger answered 1 year ago

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod...

let p = 1031, Find the number of solutions to the equation x^2 -2 y^2=1 (mod p), i.e., the number of elements (x,y), x,y=0,1,...,p-1, which satisfy x^2 - 2 y^2=1 (mod p)

Find a polynomial p(x) with zeroes at 1,-2, and -1 and such that p(2) equals 6...

Find a polynomial p(x) with zeroes at 1,-2, and -1 and such that p(2) equals 6 ? What is the remainder when the polynomial p(x) equals (x^101 - x^50 - 3x^9 + 2) is divided by (x+1) ? Find a polynomial of degree 4 with zeroes at -2, 9, and 5. (NOTE: leave your polynomial factored; please do not expand it) Factor the polynomial x^3 - 4x^2 + 3x + 2. List all the possible rational roots of the polynomial...

let p=11. find generator number for p incase of elgmal algorithm. alice selects integer number x=5....

let p=11. find generator number for p incase of elgmal algorithm. alice selects integer number x=5. calculate public and private key for Alice in elgmal algorithm. alice wants to send plaintext "AGE" to bob. assume that alice selects random k values s 6,4,7 respectively for encryption. what is the ciphertext?

1. Given f(x) = −(x − 1) 2 (x + 1) 2 (x + 5) Find...

1. Given f(x) = −(x − 1) 2 (x + 1) 2 (x + 5) Find the following a. End behavior b. Find the Zeros c. Find Multiplicity and touch or cross d. X and y intercept e. graph

5 spades, 5 clubes, and 5 hearts 1. find P(Tk+l)in terms of P(Tk) 2. find P(T3)...

5 spades, 5 clubes, and 5 hearts 1. find P(Tk+l)in terms of P(Tk) 2. find P(T3) 3. find the prob the cards are together by characters after many cuts

Let p be the prime number (2^20)*(3^7)5 + 1 = 11466178561. Solve for x such that...

Let p be the prime number (2^20)*(3^7)5 + 1 = 11466178561. Solve for x such that 2^x ≡ 2376886429 (mod p) Explain your method carefully.

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X...

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X Intercept(s) if any b) List Y Intercept(s) if any c) List Horizontal Asymptote(s) if any d) List Vertical Asymptote(s) if any e) Domain 2. precalculus

In this problem, p is in dollars and x is the number of units. Find the...

In this problem, p is in dollars and x is the number of units. Find the producer's surplus for a product if its demand function is p = 144 − x2 and its supply function is p = x2 + 12x + 130. (Round your answer to two decimal places.) In this problem, p is in dollars and x is the number of units. The demand function for a certain product is p = 123 − 2x2 and the supply...

Number of Girls x P(x) 0 0.0040.004 1 0.0330.033 2 0.1180.118 3 0.2260.226 4 0.2540.254 5...

Number of Girls x P(x) 0 0.0040.004 1 0.0330.033 2 0.1180.118 3 0.2260.226 4 0.2540.254 5 0.2250.225 6 0.1070.107 7 0.0290.029 8 0.004 Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.

Find the following probabilities a. P(X = 2) when X ∼ Bin(4,0.6) b. P(X > 2)...

Find the following probabilities a. P(X = 2) when X ∼ Bin(4,0.6) b. P(X > 2) when X ∼ Bin(8, 0.5) c. P(X ≤ 2) when X ∼ Bin(5, 0.5) d. P(3 ≤ X ≤ 5) when X ∼ Bin(6, 0.3)

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