...9— x=U, 21— x=O; while II, 14 relates to x— n= D, x — m = D. Diophantus, III, 5, 6, required three numbers such that their sum is a square and the sum of any pair exceeds the third by a square. Hence the sum of the three squares is a square, as for 4, 9, 36. Diophantus,...

...value of x in this case to be ff • The following problem represents one of the more difficult types : "To find three numbers such that their sum is a square and the sum of any pair is also a square." The results given by Diophantus for this problem are 80, 320, and 41. The most famous...

...given numbers so as to make each of them a square.1 One of the more difficult problems is as follows : To find three numbers such that their sum is a square and the sum of any pair is a square.9 Pell Equation. One of the most famous indeterminate quadratic equations is of the form This...

...added to either gives a square number. (Diophantus' answer: (3/4)2, (7/24)2.) Problem 6, Book III: Find three numbers such that their sum is a square and the sum of any pair is a square. (Diophantus' answer: 80,320,41.) Problem 7, Book III: Find three numbers in arithmetic progression...

...3, then x + 2 and x + 3 must both be squares, and he finds the value of x in this case to be $-J"To find three numbers such that their sum is a square and the sum of any pair is also a square." The results given by Diophantus for this problem are 80, 320, and 41. The most famous...

...similarly make with v. 20 a set of three. The enunciations were doubtless somewhat as follows. 19 a. To find three numbers such that their sum is a square and any one of them minus the cube of their sum gives a square. \gb. To find three numbers such that their...