Diophantus of Alexandria

God granted him boyhood for one-sixth part of his life; when a twelfth more was added, his cheeks began to sprout; he married after a seventh part, and five years later had a son. Alas, this son, dear and glorious, lived only half as long as his father, who spent four years after his son's death consoling his grief by the science of numbers.

To find three numbers such that the sum of any two of them is a square.

To find two numbers such that their sum is a given number, and the sum of their squares is also a given number.

To divide a given number into two parts such that their product is a given number.

To find three numbers such that the product of any two of them plus the third is a square.

To find two numbers such that their sum is a square and the sum of their cubes is a square.

To find three numbers such that the sum of their squares is a square.

To find a number such that if we subtract it from a given number and add it to another given number, the products are equal.

To find two numbers such that their sum is a square, and their product is a square.

To find three numbers in arithmetic progression such that the sum of any two is a square.

To find a number such that when it is added to a given number, the sum is a square, and when it is subtracted from another given number, the remainder is a square.

To find three numbers such that the sum of their squares is a square, and the sum of their cubes is a square.

To find a number such that if we add it to a given number, the sum is a square, and if we subtract it from another given number, the remainder is a square.

To find two numbers such that their sum is a square, and the sum of their squares is a square.

To find three numbers such that the sum of any two of them is a square, and the sum of all three is a square.

To find a number such that if we add it to a given number, the sum is a square, and if we multiply it by another given number, the product is a square.

To find two numbers such that their sum is a square, and their difference is a square.

To find three numbers such that the sum of any two of them is a square, and the sum of their squares is a square.

To find a number such that if we add it to a given number, the sum is a square, and if we divide it by another given number, the quotient is a square.

To find two numbers such that their sum is a square, and the sum of their cubes is a square.