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Category Archives: open problems
π/2 conjecture solved
A few posts ago I stated the pi-over-two concecture. Recently, my friend and collegue Jacek Małecki proved it in full generality. (He did it while I was on my vacation in November — sometimes it is good to take a … Continue reading
Posted in open problems
Tagged Bernstein function, contour integral, pi, representation theorem
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π/2 conjecture
The second conjecture in this blog is related to my recent work on Lévy processes. Suppose that x and y are positive reals, and is an increasing function. Then, whenever the integral makes sense, it is equal to . Although … Continue reading
Posted in open problems
Tagged Bernstein function, conjecture, integral, levy process, pi
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Heronian triangles conjecture
Let my first blog post be about my six-year-old conjecture: Every integer Heronian triangle is congruent to a lattice triangle. A triangle is said to be an integer Heronian triangle, if it has integer side lengths and integer area. A … Continue reading
Posted in open problems
Tagged conjecture, elementary geometry, heronian, integer, lattice, triangle
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JAMB 