Problem 57874. Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles

Created by Ramon Villamangca

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We define a Partial Pythagorean Triangle (PPT) as a right triangle wherein the hypotenuse and at least one leg are integers. Thus, the triples  and  represent a PPT, while ,  and  do not.
Given the limit P, find the area of the PPT with perimeter  , such that the ratio of the areas of the triangle's circumcircle to its incircle, ,  is as small as possible.
                                                              
Please present the answer rounded-off to the nearest integer.

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Last Solution submitted on Aug 15, 2024

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David Hill on 14 Jun 2023

Several tests are wrong (verified using symbolic numbers). Test 6 should be 970225, Test 8 should be 96049800, Test 9 should be 559819260, Test 10 should be 38034750625, and a suspect higher tests might also be incorrect. These results are consistent with what I expected by review of Lucas and Pell numbers.

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Problem 57874. Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles

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Problem 57874. Easy Sequences 107: Minimized Circumcircle-Incircle Areas Ratio of Partial Pythagorean Triangles

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Last 200 Solutions

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