Pythagorean Triples

Table 1

There is a relationship between the numbers in the columns on Table 1below.

Table 1

Column A	Column B	Column C
3	4	5
5	12	13
7	24	25
9	40	41
11	60	61

They are called primitive triples because there are no factors other than 1 common to all three integers.

• As you read down Column A, you notice that the consecutive numbers differ by two.

• As you move down Column B, you notice that the numbers are multiples of 4 and consecutive numbers that differ by 4, 8, 12, 16, or 20.

• As you move down Column C, you notice that the numbers are one more than the corresponding value in Column B.

Table 2

There is a relationship between the numbers in the columns on Table 2 below.

Table 2

• The value in Column A is in the form 2xy.
• The corresponding value in Column B is in the form x^2 - y^2.
• The corresponding value in Column C is in the form X^2 + y^2.

• 6 = 2 (3) (1)
• 8 = (3)(3) - (1)(1)
• 10 = (3)(3) + (1)(1)