Looking at the first 2z integers 1, 2, . . . , 2z. Choose z +...

Looking at the first 2z integers 1, 2, . . . , 2z. Choose z + 1 of them. Then demonstrate that there is at least one pair of integers from the selection that are relatively prime. (A way to approach this problem is to show that at least two integers from the selection are consecutive.)

Expert Solution

In the above problem, the case I have taken into consideration is the worst case possible, except this case we will get 2 consecutive integers before even choosing the z+1 th number i.e. when we are choosing z numbers we will have surely two consecutive integers.

Hope this clarifies, please ask for doubts in comments.

Colby Messinger answered 1 year ago

Complex Analysis: Use Rouche's Theorem and Argument Principle to determine the number of roots of p(z)=z^4-2z^3+13z^2-2z+36...

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F(x,y,z) = x^2z^2i + y^2z^2j + xyz k S is the part of the paraboloid z...

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Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z. (a) Find the directional derivative of F at the point...

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1) If x, y, z are consecutive integers in order then 9 | (x+y+z) ⟺ 3...

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