() 2p n! (a) (") = 2 (mod p), where k for 0

Q: Find all the solutions of the congruence equation x6-2x5= 35 (mod 6125).

A: Consider the given congruence equation. x6-2x5≡35mod 6125. Now, the prime factorization of 6125 is:…

Q: Trail 1 Trail 3 -H- H-- Trail 4 Trail 2 A park has a system of trails for walking and biking. Trail…

A:

Q: a + bi form modulus argument —3 — 3і - — 2 — Зі $1 · $2

A:

Q: 4. Solve the following quadratic congruences: 5x² + 6x + 1 = 0 (mod 23)

A:

Q: Evaluate the deteminat of each matris. A= 5-1 [213 3. A-I0 2 20-2 4 A 6 0

A:

Q: Let G={1,-1,i,-i} with usual multiplication then G is isomorphic to Select one: a. Z, x Z, b. (Z, +)…

A:

Q: а). Solve the linear congruence of 231x = 147 mod 598 .

A:

Q: Which of the following linear congruence has 2 incongruent solutions? (a) 3x = 9 (mod21) (b) 14x =…

A: to solve linear congurence , ax≡b(mod m) .........(1) the first stem is to reduce the congurence  by…

Q: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: x + y)(z + w) = xz + xw + yz + yw A.) Explain in your own words what this problem is asking. B.)…

A:

Q: Solve the following quadratic congruences: (a) 3x² + 9x + 7 = 0 (mod 13) (b) 5x² + 6x + 1 = 0 (mod…

A: According to Q&A guidelines, I can answer only one question. So I answered (a).

Q: Determine the system of linear congruences which yeild all the square roots of 31 modulo 33.

A: Please find the answer in next step

Q: (O Show that AdditPon closed i's a binasy binazy operation of the Set sver Real num beð and Complex…

A: The objective is to show that addition is a closed binary operation over the set of real number and…

Q: вршио Show that a group by of ordag pq for district prime p is solvable.

A:

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: FOR ANY TWOCOMPLEX NUMBERSZ, ANDZ,,PROVE THAT |Z|+|Z,|=,(Z, +Z,)+ /Z,Z» +÷(Z, +Z»)- Z,Z, .

A: for two complex number Z1 and Z2 prove that Z1+Z2=12Z1+Z2+Z1Z2+12Z1+Z2-Z1Z2

Q: Let ---0--0 8 u= W= Compute 3w+6u = -131

A:

Q: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: Explain why the following linear congruence has no solutions:   5x ≡ 16 (mod 45).

A: Explain why the following linear congruence has no solutions: 5x ≡ 16 (mod 45).

Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

Q: ind all solutions of the linear congruence: 9x = 5 mod (14)

A:

Q: Find all solutions of the systems of congruences: = 12 (mod 25) 22 (mod 35).

A:

Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

Q: find the congruence for the following congruence equations: (1) 18x=3 (mod47)

A: First and second question are independent .So According to guideline I am solving first one.The…