MATH STINGER #45
by Dr. Joel C. Fowler
Assistant Professor of Mathematics

 

 This issue's puzzle is the following. A standard set of integer values for a right triangle is 3, 4, and 5. These work because 3^2+4^2=5^2 in the Pythagorean Theorem. This leads to several puzzles: 1) Find all sets of consecutive positive integers that satisfy the Pythagorean Theorem? 2) Find all sets of consecutive positive integers a, b, and c that satisfy a^3+b^3=c^3? 3) Find all sets of consecutive positive integers a, b, and c that satisfy a^4+b^4=c^4? A correct answer to the above should include, in addition to any sets of integers that satisfy the equation, an explanation as to why there are no others.

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