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A classic unsolved problem in number theory asks if there are infinitely many pairs of `twin primes', pairs of primes separated by 2, such as 3 and 5.
Let m be the least common multiple of a and b, and let c be a common multiple of a and b. Show that m divides c.
Knowing that {Hn}, n = 0, 1, 2... are orthogonal and with respect to a suitable weight function p(x), write down first two orthonormal Hermite polynomials.
After eating at the restaurant, keith, Sandy, and Jason decided to divide the bill evenly. If each person paid 26 dollars, what was the total of the bill?
Explain in your own words your understanding of the concept of slope as it relates to graphs of linear equations. Illustrate with examples
Why do intersecting lines represent a unique solution? Give examples to support your answer.
The aim of this exercise is to prove that the Mordell equation y2 = x3 - 5 has no solutions. We proceed by contradiction and assume that (x, y) is an integral.
Solve by substitution or elimination method:A university bookstore recently sold a wire bound graph-paper notebook for $2.50
Prove that if p is a prime number of the form 4n + 1 , then the following congruence holds,x2 =- 1mod p
Proof of diagonalizability.If A is diagonalizable and B is similar to A then B is also diagonalizable.
Associated two linearly independent eigenvectors: If you have a floating point number ending in e-16 or some such thing
Deduce that the Prime number Theorem can be expressed in the form p(x)˜li (x).
Determine the normalized eigenfunction for this problem;Use the results in part (a) to express f(x)=x in an eigenfunction expansion
Solve the inequality. Write the solution in interval notation and graph the set on the number line. -2(x - 4) 3x + 1 - 5x
Gradient, Divergence and Curl (II).Real Analysis Gradient, Divergence and Curl (II)
Can you help me answer question by explaining each step please?Find the eigenvectors and eigenvalues of the matrix
Emile and Gertrude are brother and sister. Emile has twice as many sisters as brothers, and Gertrude has just as many brothers as sisters
By considering appropriate series expansions, prove that the power series expansion of the product of the (infinitely many) exponential factors.
Solve the system of equations by the addition/subtraction method. Make sure you the necessary 5 steps are included.
Write an expression to model the total cost and then evaluate the expression for 1 to 5 months of internet access.
Jerimiah runs 35 miles per hour. Write an algebraicexpression to show how far he runs in h hours.
Matrices : Row Operations and Echelon Form.An augmented matrix of a linear system has been reduced by row operations to the following form.
System of Equations : Software Techniques and an Example.Many free software mathematics packages on the Internet will solve a system of equations
Compare the Richter scale and Mercalli scale. In your opinion, explain which is more meaningful in the use of reporting earthquake destruction.
Provide one example to show how you can use the Expected Value computation to assess the fairness of a situation (probability experiment).