Elementary algebra sign). One of the most well-known equations describes Pythagoras' law relating the length of the sides of a right angle triangle: This equation states that formula_44, representing the square of the length of the side that is the hypotenuse (the side opposite the right angle), is equal to the sum (addition) of the squares of the other two sides whose lengths are represented by formula_45 and formula_46. An equation is the claim that two expressions have the same value and are equal. Some equations are true for all values of the involved variables (such as formula_47); such equations are called
Fermat's right triangle theorem that the numbers to be squared are the difference of legs, hypotenuse, and sum of legs of a Pythagorean triangle, and that the congruum is four times the area of the same triangle. In his later work on the congruum problem, published in "The Book of Squares", Fibonacci observed that it is impossible for a congruum to be a square number itself, but did not present a satisfactory proof of this fact. If three squares formula_4, formula_5, and formula_6 could form an arithmetic progression whose congruum was also a square formula_7, then these numbers would satisfy the Diophantine equations That