38.7. Consider the system of congruences x = a1 (mod m1) x = a2 (mod m2) where mi and m2 are relatively prime. Let bị and bz be integers where bị = m¡ b2 = m7' in Zm2 in Zm - Hon 39 Finally, let Xo = m¡bja2 + mzbza1. Please prove that xo is a solution to the system of congruences.

Q: 2. Find every k (mod 60) such that the system of congruences x = 6 (mod 30) = k (mod 60) has more…

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Q: 1. The remainder of p(x) = x² + ax³ + bx² + 5x by x² + 3x + 2 is -3. Find a, b 1 divided

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Q: 7) Note that -2 is a square modulo 11. Indeed, 82 +2 = 6.11. Use this information, and the method of…

A: To use method of descent to construct a solution of x2+2y2=11 Now, it is known that -2 is a square…

Q: 8. We know that P₁ = P2 on B if P₁ = P₂ on C, provided that C generates B and is a 7-system. Show…

A: From the given information, P1=P2 on B if P1=P2 on C provided that C generates B and is a π system.…

Q: Qn+1=2Qn-bn+2 bn+1=-Qn+2bn-1 Q0=0 b0=1 find the rule of serie

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Q: 4 7 2 Let M-[and A-and-]-[3] B= 7 Express M as a linear combination of A and B and C 1) M=3A-2B+C 2)…

A: Given that the matrices  M=4779 , A=1111   , B=1234  and C=1145 .

Q: 3) x² + y² + 16x+10y+80= 0 2 CXA6 2 5) x² + y² - 22x+26y +254 = 0

A: Here we have to find the standard form.

Q: 1. Find all x, y, and z such that a) x = 3 (mod 4) x = 5 (mod 21) x = 7 (mod 25) b) 3y = 9 (mod 12)…

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Q: 9. Which of the following is the simplest form ofV48? A 16V3 10. How will you simplify 5V3 + V12? A.…

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Q: 1. Find all solutions of the system of congruences x = 4 (mod 5), x = 5 (mod 6).

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Q: ). Hence, solve for the system below 7x + 3y = 10 (mod 16) 2x + 5y = 9 (mod 16)

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Q: Let gcd (a,m) = 1 then the solution of the linear congruence ax = b (mod m) x = a(p)-¹b (mod p) x =…

A: Introduction: The greatest common divisor of two integers is an integer that divides both of the…

Q: 8. We know that P₁= P2 on B3 if P₁ = P2 on C, provided that C generates B and is a 7-system. Show…

A: Solution :-

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

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Q: b) iv)

A: Part 2: Explanation:Step 1: Identify the contour C:The contour C is defined as the set of complex…

Q: 10. Let m and n are two positive integers with m > n. Let a be a positive integer. Prove that a2" +1…

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Q: 11. Solve the systems of congruences: a. x = 7(mod 11), x = 4(mod 24) b. 3x = 11(mod 17), 2x = 3(mod…

A: The given problem is to solve the given system of congruence equations. Given system of congruence…

Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

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Q: Solve the systems of linear congruence equations.

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Q: 7. Solve the congi 8. Solve the system of congruences x = 3(mod 7) x = 5(mod 8) lid?

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Q: At the imaginary university e/UT there are 101 students in their first year at M&CS. In their first…

A: Given: Double counting Total students=101 To find: k

Q: 3. Find all solutions of the system of congruences (mod 12), (mod 10). x = 5 x = 8

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Q: (3) (a) Find the smallest positive solution of the system of linear congruences x = 3 (mod 5) * = 7…

A: We solve this using Chinese Remainder Theorem

Q: Solve the system of congruences r = 1 mod 10 = 2 mod 7

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Q: 13. Suppose that z1 V3 +i and z2 = 2/2+ 2v2i. 22 (a) Write z1 and z2 in mod-arg form. (b) Hence…

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Q: O 4. Find the LCM of 4bc2, 4a?-36b2, and ax? + bx + c. O 4bc² (a + 36) (ax? + br +c) O 4bc (a +…

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

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Q: (b) Consider the system of linear congruences below: x = 2 (mod 5) 2x = 22 (mod 8) 3x = 12 (mod 21)…

A: As per bartleby guidelines, for more than one questions asked, onlyone is to be answered, kindly…

Q: he output ((PV¬r) ^¬q) v (p ^ (q V r)) from input bits p, q and r.

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