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Prove that there are no integers x, y, and z such that x2 + y2 + z2 = 999. Provide complete and step by step solution.
16 is a non-trivial square root of 1 modulo 51; hence 51 is composite, 7 is a non-trivial square root of 1 modulo 47; hence 47 is composite
We may assume that r and s have no prime factors in common, since any common prime factors may be cancelled.
Step by step solution to this problem, starting off with how does one determine the values of x and y.
If a deck is rectangular and has an area of X2 + 6x + 8 (the 2 is squared) square feet and a width of x + 2 feet. Determine the lengths of the deck.
Express x1, x2, and L(x) in terms of polar coordinates. Describe geometrically the effect of the linear transformation.
Let f be a nonnegative integrable function. Show that the function F defined by F(x) = -8?x f is continuous by using Monotone Convergence Theorem.
Difference between mapping R3 to R2 and the reverse. What's the difference between mapping from R3 into R2 and mapping from R2 into R3?
Is it possible for an extremely large prime to be expressed as a large integer raised to a very large power? Explain.
Industrial Application Images.The two images below shows one of our attempts to come up with the rotation angle required. I
In 1997, there were 3043 county governments in the United States. Of these, 3 were in Delaware. What was the ratio of county governments.
Using the fact that 1+x = 4+(x-3), find the Taylor series about 3 for g. Give explicitly the numbers of terms. When g(x)=square root of 1+x
Modify Euclids proof that there are infinitely many primes. First, prove that any number of the form 4n - 1 has a prime factor which is of the form 4k - 1
Show that b is then the largest square dividing n. (A square-free integer is an integer that is not divisible by any square > 1).
6301 is prime. If x, y, and z are integers that are not divisible by 6301, which of the following is equal to x^6299.y^12600.z^18903 mod 6301 ?
Show that there are exactly (p^2-p)/2 monic irreducible polynomials of degree 2 over Z_p, where p is any prime.
Discuss an element of drinking water where you see a public health gap or need that should be addressed.
What is the interest rate?, b. find the exponential growth function, c. what will the balance be after 10 years ?, c. when will the $ 2,000 double?
Systems of Linear Equations: Word Problem.Please help with the following problem that involves systems of linear equations.
The degree three polynomial f(x) with real coefficients and leading coefficient 1, has 4 and 3=I among its roots.
Linear Systems of Equations: Gauss-Jordan Method.Solution of Linear Systems by the Gauss-Jordan Method
Nonisomorphic Central Extensions.Describe all nonisomorphic central extensions
Linear Alegbra: Span of Dimension.What is the span of the dimension
Linear Algebra: Find a Vector in a Basis.Find the coordinates of this vector (polonomial) in the basis {1-x,1+x,x^2-1}
List all irreducible polynomial of degree 2, 3 and 4 over F 22 j u u 2 3 3 2. Prove your assertion.