3) If the gcd(z,n) = d and xz = yz mod n then: Show that x = y mod

Q: Given 6x + 2 ≡ 101 (mod 7), find an integer z such that 2x ≡ z (mod 7)

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Q: If a = b (mod m) and a = b (mod n) then a = b (mod mn)

A:

Q: Let a, m € Z+ and (a,m) = (a - 1, m) = 1. Then prove that 1+a+...+ a(m)-1 = 0(modm)

A: For given,       (a,m) = (a -1, m) = 1 We have to show,      1 + a + a 2 + ........ + a φ (m)-1 ≡ 0…

Q: Calculate C(12,5) by hand. As C(n,r) = n!/(n-r)!r! identify n and r, and write out every number in…

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Q: 2. Let a be a positive integer. Explain why the linear congruence ax = b (mod a + 1) has a solution…

A:

Q: Find all Pnterers x such that 5x=12 (mat) LoxE 4 (mad) 7x=16 (modlo) and 1o00s x3000

A:

Q: If al = b (mod p), then prove that a = b (mod p).

A: (ii) given that                                                ap≡bp   (mod p) we have to prove…

Q: Show that if a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m).

A:

Q: Find the GCD (90, 36).

A: Given numbers are (90,36). The factors of prime factor of 90 are (2,3,3,5) The factors of prime…

Q: Using y=2x-1 (mod26),  1. encode GGWP 2. decode IY

A: First, find the numerical equivalent of each letter. Then, use the formula to encode the letter.

Q: Find all x EZ221 such that x2 =97 (mod 221).

A: To find : all x∈ℤ221 such that x2≡97mod 221 Pre-requisite : Properties of Legendre symbol - 1. ap=1,…

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

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

Q: Find  mod (59, 10) and div (59, 10).

A:

Q: If a =b (mod m) then a" = b" (modm) Vn e Z*.

A: Given a≡bmod m. we have to show that an≡bnmod m. we wil prove this by result by using method of…

Q: Show that y = x (mod p) leads to -y = -x (mod p).

A:

Q: If a+c=b+c (mod m) then a =b (mod m) Select one: True False

A:

Q: Find all integers sx such that 2x = 5 (mod 7).

A:

Q: Suppose a is divisible by b. Show that gcd(a, b) = b.

A: Consider the given information. As we have given that a is divisible by b. then there is a number c…

Q: Find the nonnegative integer a less than 28 represented by each of these pairs, where each pair…

A: According to the given information, it is required to find the non-negative integer a less than 28…

Q: If gcd( m, 91) = gcd( n,91) = 1 then show that 91|m³7 – n37 %3D

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Q: Ifx= y (mod n) and u =v (mod n) then which of the following is false. (a) x+u= y+ v (mod n) (b) хи в…

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Q: Let x, y ∈Z. Prove that if x≡1(mod 5) and y ≡2(mod5 ), then x^2-y^2≡0(mod 5).  Give 2 examples to…

A: Given, x,y∈ℤ and x≡1mod 5, y≡2mod 5

Q: Show that if x mod 8 = 1, then (3x −5) mod 6 = 4.

A: Solution

Q: 6. Give the addition and multiplication tables for nonconstant polynomials in Z3[x]/(x² + x+2).…

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Q: Let (a,b)=1 Show that (a+b, a-b)=1 or 2. When is this GCD 1? When is 2?

A: Proof:It is given that gcd(a,b) = 1. So ax + by = 1.Let gcd(a + b, a – b) = d, then d|( a + b) and…

Q: 1) a. The number of mobile phones made by Finland has the following probability distribution: А 2 +…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.