MathDB
2022 A Individual #21

Source:

April 28, 2022
2022 A Individual

Problem Statement

Let T(p)T(p) denote the number of right triangles with integer side lengths and one of its side lengths being pp. Which of the following values of pp produces the greatest possible value of T(p)T(p) among all five answer choices?
<spanclass=latexbold>(A)</span>24<spanclass=latexbold>(B)</span>27<spanclass=latexbold>(C)</span>28<spanclass=latexbold>(D)</span>36<spanclass=latexbold>(E)</span>54<span class='latex-bold'>(A) </span>24\qquad<span class='latex-bold'>(B) </span>27\qquad<span class='latex-bold'>(C) </span>28\qquad<span class='latex-bold'>(D) </span>36\qquad<span class='latex-bold'>(E) </span>54