Question

The table of exercise 1 suggests that one of the numbers in any primitive Pythagorean triple is divisible by 4, one is divisible by 3 and one is divisible by 5. Please Prove this

Answer 1

Please keep in mind that the numbers in all primitive Pythagorean triple are not necessarily that one is divisible by 4, one is divisible by 3 and one is divisible by 5.

Here is an example that shows the argument is not correct for all  primitive Pythagorean triple

(5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), (12, 35, 37), (9, 40, 41)

These all are primitive Pythagorean triple but see in first on two numbers are divisible by 4 and 5 respectively but the last one is not divisible by 3.

Similarly in a second primitive Pythagorean triple two numbers are divisible by 4 and 3 respectively but the last one is not divisible by 5. And so on

So the above argument is not valid for the general cases.

Ask if you have any quarries. Thank you