arXiv subjects
Publications and source records attributed to Yasushi Ieno.
A research for a general expression of the triplets of integer sided triangles with a $120^{\circ}$ angle, in parallel with the case of a $60^{\circ}$ angle.
The set of terms of an infinite sequence expressed by a recurrence relation is equal to the set of maximum numbers of all primitive Pythagorean triples such that the difference between the two non-maximum numbers is 1, which Cimmino showed. By reference to Cimmino's researches, we show a recurrence relation for the case where the difference between the two non-maximum numbers is not 1, but 7.
There exists "a square problem": in a unit square is there a point with four rational distances to the vertices? This problem is still regarded as unproved. Yang showed proofs for several special cases of the square problem. By the reference of Yang's researches, We have proved other special cases of this problem.
A newly-generalized problem from a problem initially thought for the Mathematical Olympiad and the methods to solve it.
The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, is called 'the grasshopper problem'. To this problem Kos developed theory from unique viewpoints by reference of Noga Alon's combinatorial Nullstellensatz. We have tried to solve this problem by an original method inspired by a polynomial function that Kos defined, then examined for n=3, 4 and 5. For almost cases the claim of this problem follows, but there remains imperfection due to 'singularity'.