SOLUTION: The general formula for Pythagorean triples is {{{ a=m^2 - n^2 }}}, {{{ b=2mn }}}, and {{{ c=m^2 + n^2 }}} for integers m and n. Use the formula to find all the primitive Pythagore

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Question 1055337: The general formula for Pythagorean triples is , , and for integers m and n. Use the formula to find all the primitive Pythagorean triples containing 24 as one number.
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
{7, 24, 25}
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
The general formula for Pythagorean triples is , , and for integers m and n.
Use the formula to find all the primitive Pythagorean triples containing 24 as one number.
~~~~~~~~~~~~ 


24 = 2mn ----> mn = 24/2 = 12  ----> 


     (m,n) = (1,12)  gives the Pythagorean triple  (24,143,145).


     (m,n) = (3,4)   gives the Pythagorean triple  (7,24,25).


There no other primitive Pythagoren triples.


Solved, answered and explained.

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See also this web-page

https://en.wikipedia.org/wiki/Pythagorean_triple



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