It is easy to show thát 3 iš nót thẻ sum óf thẻ squares of 2 integers, i.e. a² +b² + 3 any integers a and b. Prove that there are infinitely many such integers that cannot be written as the sum of the squares of two for integers.

Q: Consider nonnegative integer solutions of the equation xi + x2 + x3 + x4 + x5 + æ6 = 30.

A: The non-negative integer equation is x1+x2+x3+x4+x5+x6=30Since ,xi-number varying from 0 to…

Q: Determine whether the given set is linearly dependent or linearly independent: S =

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Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: In(2x² – 2) = In- 2x2 = 2 In x 2. True False

A: Check whether ln2x2-2=ln2x22=2lnx is true or false as follows. Recall, ln(a)-ln(b)=lnablnxa=alnx

Q: 3 3x2+2x+1 3. Compute dr 2 x2

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Q: Show that the square of any positive Integer is of the form 3m or 3m+1 for some integer m

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Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: 1) Show that the square of an odd integer is odd. 2) Show that the product of two odd integers is…

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Q: Qing is twice as old as Rayna. Qing is 4 years younger than Paolo. The average age of Paolo, Qing…

A: Since you have asked multiple questions, we will solve the 1st question for you. If you want any…

Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

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Q: I am thinking of a three-digit number. All the digits is odd, the ten's digit is a perfect square,…

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Q: a. Find all pairs of integers such that one is a multiple of 7 and the other is a multiple of 11 and…

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Q: 2. Expand by multiplying 'o) a) (3x+ 4)(2x - 2) b) (2x - 7)(-4x + 5) c) -4y(-4x -5y)

A: Given  a) (3x+4)(2x-2) Multiplying,  (3x+4)(2x-2) = (3x)(2x-2)+4(2x-2)…

Q: Let A - -5 -2 -5 -10 -5 -7 -20 -7-22| Solve the equation using an LU factorization of and b - Ax = b…

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Q: 8. Let a, b and c be any positive real numbers. Prove that b² + c² a²+b² 2c a² + c² + 2b 2a > a+b+c.

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Q: 2. Which of the following binomials is a factor of the quadratic expression, three x-twenty-six x +…

A: Consider the quadratic expression: 3x2-26x+16

Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

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Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: Find all the zeros and their multiplicities of x5 + 4x4 + 4x3 - x2 -4x + 1 over Z5.

A: Residues and zeroes of the polynomial

Q: Find a counterexample to show that each of the statements is false.

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Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: ans 1. %3 4x+ 2 9x-3°

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Q: Find the number of nonnegative integer solutions to x₁ + x₂ + x3 + x4 + x5 ≤ 23. Find the number of…

A: We have to find the number of non negative integer solution of Note: According to the guidelines we…

Q: If (2x-1) is a factor of the polynomial p(x)=2x^3-3x^2+kx+6, then the value of k is: a) k= -6 b)…

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Q: 4. Factor a? + 12ab + 32b2. OA. (a+4b)(a + 8b) О в. (а - 4b)(а - 8b) С. (а - 4b)(а + 85) D. (a +…

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Q: Prove that the sum of the squares of two odd integers cannot be the square of an integer.

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Q: Find positive integers that satisfy x + y + z = 6 x + 5y + 8z = 35 x = i ! y = i

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Q: the number of nonnegative integer solutions to (x₁ + x2 + x3 + x4 + X5) (X6 + X7 + x8 + x9 + x10) =…

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