7. Prove that if n is odd, then 2 is not a square in GF(5") In other words, prove that there is no element a e GF(5") with a² = 2.

Q: Calculate M, for f(x) = 6 · In(æ³) over [1, 2]. M6 ||

A:

Q: 1b) Given yadrilateral KLMN with K(-,4),L (2,2),Mlo-1) and NC-3,1). Verify that KLMN is a Square,…

A: Given: A quadrilateral KLMN with K(-1, 4), L(2, 2), M(0, -1) and N(-3, 1). To verify: The given…

Q: Prove: For integers m, n, 12mn – 9 is an odd integer.

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Q: 4. Prove that for n > 0: E, 2* = 2"+1 – 1. sk3D0

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Q: 5. Show that Z[V-6] is not a UFD by factoring 10 in two ways. Why does this prove that Z[V-6] is not…

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Q: (2) Prove by contradiction that if 3z2- is irrational then r is irrational. 215

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Q: Show with the help of Fermat’s little theorem that if n is a positive integer, then 42 divides n7 −…

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Q: Prove that the K4 is not consecutive.

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Q: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Show that 3n^ 2+8nlogn is big-Oh (n ^2 )

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Q: What is the smallest positive integer k such that xk = e for all x inU(7 . 17)? Generalize to U(pq)…

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Q: Prove for all mEw and n E w, we have that m+ ·n=m・n+n.

A: Given that m,n∈ω. To prove: m+· n=m·n+n

Q: 3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no…

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Q: 4. Prove that the difference between the square of any odd integer and the integer itself is always…

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Q: () is even. 3. Prove that for all positive integers n, the number

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Q: 2. Prove that L(cashkt)= ki 52-K2

A: To prove that  L(cosh(kt))=ss2-k2

Q: 2. Count the number of rearrangements of the word TASTE in which no letter appears in any of its…

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Q: 4. Prove that if m and n are positive integers and x is a real number, then %3D m

A: We know ⨽x⨼ = x if x is an integer. Here, since m and n are integers, we have the following steps:…

Q: Suppose the product of 22 integers is equal to 1. Prove that their sum is not equal to 0.

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Q: 11. Prove that if n is a perfect square, then n + 2 is not a perfect square.

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Q: 3. Prove by contradiction, that if x and y are odd integers, then there is no integers z such that…

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Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: 42 Show that E a Imod n) for all integer aif and only if n is squarefree. Ep(n) is Euler Totient…

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Q: Theorem = 7 K 51 M 25

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Q: Suppose that m, n are two integers such that m 2n2 = 1. Does it follow that m and n are relatively…

A: Given that m, n are two integers such that m3-2n2=1. To show m, n are relatively primes we have to…

Q: Show that if n e Z is a perfect square such that 3|n, then 9|n.

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Q: Prove that if n is a perfect square, then n +2 is not a perfect square.

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Q: 2. Show that if x and y are perfect squares (that is, x = m? and y = n2, where m and n are…

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Q: Verify S Tokes' Theorem To 2.

A: Introduction: We know that stoke's theorem is given by the formula, ∮CF.dr=∬s2∇×F·n.dσ

Q: 15.5 Prove that if n is a perfect square then n = 4q or n = 4q + 1 for some q e z. Deduce that…

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Q: prove the difference of the squares of two z integers is always divisible by 16 (i.e. z1^2 - z2^2 =…

A: We prove that (z_1)^2-(z_2)^2=16k for some integer k, then we say that divisible by 16.

Q: Is there a km. lenRit 3 Why 3 kM. X4-2x If there is a konft prove 9t by using the (E-8) defnti9on of…

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Q: s) Express the infinite contimod fraction [2, 1,5 quadratic irrational- as a ity.

A: We need to express the infinite continued fraction 2, 1, 5¯ as a quadratic irrationality. The…

Q: Suppose that m, n are two integers such that m3 – 2n2 = 1. Does it follow that m and n are…

A:

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: Show that th equation x" + y² = z" (mod 5) has nonzero solutions in Zz if and only if n is odd.

A: Given: xn+y2n≡zn(mod 5)

Q: Let m and n be positive integers and let k be the least common multipleof m and n. Show that mZ∩ nZ…

A:

Q: Apply Gauss forward interpolation formula to obtained y(39) if 15 30 45 60 75 90 Y : 0.23 0.32 0.33…

A: Thanks for your question. Since your question contains two parts, so we are solving the first part…

Q: Show that E(x-a) = E(x; -x) + n(x- a), squares about a = is smallest. other words, show that the sum…

A: The answer is as follows :

Q: 6. Show directly that inf(B) = 1 for B {N =: 4+1} -

A: The given expression is,  B = {1+1/n : n belong to N}

Q: 2. Prove that if m and n are integers and mn is even, then m is even or n is even.

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Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

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Q: Prove (NOT BY EXAMPLE) that for every nonzero integer, its square is positive.

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Q: Show that Zn has a nonzero nilpotent element if and only if n is divisibleby the square of some…

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Q: Prove directly from the definitions that for all integers the Same parity Divide Bnt 19. and E m and…

A: If m an n are both even  let m= 2a and n= 2b   then  5m+7n=5(2a)+7(2b)=10a+14b=25a+7b therefore,…

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: 7. Find a direct way of showing that the (2, 2)-entry of a 3 x 3 magic square with weight w must be…

A: Use the common form of 3×3 square matrix with weight w  to find (2,2) entry

Q: 4. Prove that an element r of Z2 \ 2Z2 is a perfect square if and only if x = 1 (mod 8).

A: we prove first part⇒let x∈Z2\2Z2 is a perfect square whereZ2\2Z2…

Q: 2 There are integers m and n such that m² +n² is a perfect square.

A:

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.