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Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

Serre's problem, also called Serre's conjecture, asserts that the implication "free module ==> projective module" can be reversed for every module over the polynomial ring ...

Honaker's problem asks for all consecutive prime number triples (p,q,r) with p<q<r such that p|(qr+1). Caldwell and Cheng (2005) showed that the only Honaker triplets for ...

Find the figure bounded by a line which has the maximum area for a given perimeter. The solution is a semicircle. The problem is based on a passage from Virgil's Aeneid: "The ...

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

With three cuts, dissect an equilateral triangle into a square. The problem was first proposed by Dudeney in 1902, and subsequently discussed in Dudeney (1958), and Gardner ...

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...