Find x ∈ Z so that x^3 ≡ 15 (mod 7^4 ). Use the lifting method.

Q: Show that x = 1 is the only zero of the polynomial x^25 − 1 over Z_37

A: The elements of the sets Z37 are {0,1,2,3,.......,36}

Q: Find LOVE LOVE 0 0 [Trysin(x² + y²) dady

A:

Q: value of ∑n=1∞(6an+9bn) if ∑n=1∞an=8 and ∑n=1∞bn=2.

A:

Q: Which of the following statement is true in ZZ? O O O (0=1+x)^AXE (0=A+X)^EXA (0=1+x)^AXA None of…

A: We want to find true statement.

Q: Compute √27 using once False Position method with x₁ = 1 and x = 2. A 1,69 B 1,84 1,93 1,78

A: We have to compute 275 using the method of False position once where xl=1 and xu=2

Q: We know that x^2= 2(mod 112) and try to find the solution of x

A: This is a problem of Number Theory.

Q: Compute ATBT and BT AT by hand if possible. If not possible, describe why. A = 2 3 −1 0 B = 10 -1 0…

A:

Q: Decrypt the message "PYZTP" which was coded using the key f(a) 19a +1 mod 26. Provide full details…

A:

Q: Use the given real ZERO of the polynomial function to find the remaining real ZEROS. f (x)= 380x² +…

A:

Q: Prove that ithe polynomial PCO =-2xP +2x2+loxx t6 has and fachor azero at M= 3, and fachm s ala the…

A: The given polynomial is px=-2x3+2x2+10x+6. It is given that x=3 is a root of the polynomial. If x=3…

Q: 22/By using Newton's backward difference formula, construct an interpolating polynomial from the…

A:

Q: Which of the following polynomials is reducible over Q? * x^4+x+1 O 3x^2+x+2 3x^3-6x^2+x-2 None of…

A:

Q: Drove: am t (att)" =1 +a(it()m=) Cmod acate) Where a, ore integers. n

A:

Q: x^4 + 2x +12 = 0( mod24) All that is not equivalent to polynomial congruence Find solutions.

A: We must identify values of that fulfill the congruence equation x^ 4 + 2x +12 ≡ 0 (mod 24) in order…

Q: What is the coefficient ot x" in (x+3) '9? What is the coethicient et x? in the expanson ot lx +2) 4…

A: Binomial theorem expantion

Q: [a] z = dz dr D 4+4-³ P d/y +2 = (4+48-8³) a (x³/2) - 83/2 d (4+48 -√3) (4+48-83)2 3 (4+48-8³) 50 -…

A:

Q: Find the gcd of (x^4+x^3+x^2+2x+3) and (x^3+4x^2+2x+3) in Z5.

A:

Q: Prove a^2 +4a+3 is odd if and only if a is even.

A:

Q: Find the recursion formula and a fourth degree polynomial approximadion for the power serîies…

A:

Q: Prove the claim that there are no integers j and k such that j^2 + 3k^2 = 8

A: Since both j and k are being squared so if we prove the case for positive integers, that will prove…

Q: How would you use the existence and uniqueness theorem here?

A: Here the given initial value problem is,.Existence and Uniqueness theorem :The solution of an…

Q: Let g(x) 3 +x+7. = X i) Find a solution to g(x) in Z/21Z. ii) Find a solution to g(x) in Z/3969Z…

A: We will use the basic knowledge of polynomials and congruence to answer this question and its both…

Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

A:

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A:

Q: Please help quick thanks

A:

Q: V10 r (Vx² + I – Væ² – 1) - - V5 Vx4 – 1

A:

Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: Show that 1 + i is a root of x* - x' + x2 + 2. Use this fact to decompose the polynomial into a…

A:

Q: Suppose there is a currency which only uses 3-cent coins and 7-cent coins. Prove that for all…

A:

Q: a) Factor a* + a3 +x into irreducible polynomials in Za[z]; b) Find the multiplicative inverse of…

A: The multiplicative inverse of (x2+1) in given ring is square (x2-1). For justification locate step 2…

Q: OUp3 Fee/X = 0

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Why the minimal polynomial x^2 - (sqrt(2)+sqrt(-2)) splits into linear factors over K?

A: Assume K is a field that includes the square roots of both 2 and -2. The formula for the element  α=…

Q: Exercise #1: Evaluate the following, given the values A-12, B=3, C-6, D-2: a. F= A+B/C-D^2 b. F=…

A: B/Cand B\C What do these signify? we shall evaluate the part c. we have, F=A+BMODC And A MOD…

Q: (4) 9Afi - fiAgi (a) Show that A 9i 9i+1

A:

Q: Explain why 3Z is not an ideal in Q

A: