Here's another rule for generating Pythagorean trianges,

Last time each triangle began with an odd number. This time we will use even numbers:

4, 3, 5 | (16 + 9 = 25) |

6, 8, 10 | (36 + 64 = 100) |

8, 15, 17 | (64 + 225 = 289) |

You generate first number of the next line by writing down the next even number. To find the second and third numbers, add the first number to the second number in the previous row. The second and third numbers are one before and one after the result. For example, in the second row above, the first number is 6 as it is the even number that comes after the first number in the row above it, which is 4. We then add this 6 to the second number in the row above, which is 3. This gives us 9. The second and third numbers are one either side of this: 8 and 10.

Let's find the next row. The last row begins with 8. The even number after 8 is 10. So this is the first number:

10

Add this 10 to the second number of the previous row, which is 15. 10 + 15 = 25. The second and third numbers are one either side of this: 24 and 26

10, 24, 26

10

^{2} + 24

^{2} = 100 + 576 = 676 = 26

^{2}
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