Given that (1 + tan 1)(1 + tan 2). . .(1 + tan 45) = 2n, find n

In how many ways can 8 white rooks be placed on an 8x8 chessboard such that the main diagonal of the board is not occupied?

Let ABC be an isosceles triangle with AB equal to AC, and M the midpoint of side BC. Consider a point E outside the triangle such that the distance BE is equal to BM, and the distance CE is equal to CL, where L is the intersection of the perpendicular bisector of segment AB with the circumcircle of triangle AMB, on the same side as A with respect to BE. Point F is the intersection of the perpendicular bisector of segment AB with the circumcircle of triangle AMB. Show that angle FME is equal to 90°

Find all functions such that

Let DYC be the circumscribed circle of triangle DYC. Three tangent lines are drawn through D, Y and C, such that the lines passing through D and Y are perpendicular at A. Let B be the intersection of the tangent of Y and C. DX is drawn in such a way that AX = BY. Show that angle XDA = angle CDY.

Prove:There are no integers x, y, that y^2+9998587980=x^3.

Find all positive integers and such that:

A positive even integer is called stylish if the set can be partitioned into pairs such that the sum of the elements in each pair is a power of . For example, is stylish because the set can be partitioned as , with sums , , and respectively. Determine the number of stylish numbers less than .

"All the diagonals of an 11-gon are drawn. How many quadrilaterals can be formed using these diagonals as sides? (The vertices of the quadrilaterals are selected from the vertices of the 11-gon.)"

Range of function