# Thread: The Answer of my Professor Challenge!

1. hi all,..
i posted from few days topic says my professor challenge,..and i tried to solve this out but i didnt get it,..but my friend gut it
the question was saying:
find all pythagriam Triples (with no common division between a,b&c).(i wasnt so clear in presenting the q in the last topic so here it is again )

well my friend shoot that:

*****************

a number (n) : squared minus 1,4 can NEVER give a number (n) : squared..
example 9- 1= 8, 9- 4= 5

so there is No common factor that: (c) is Odd: Csq
To divide an odd no. squared : is odd into 2 nos.: squared, one square must be even and the other sjould be odd..

Now let Asq be odd and B sq be even so: A is odd and B is even.

somehow b is always equal to C- 1
so the problem is in A:
so we can made the form like:

A B C

3 1(3+1) 1(3+1) +1
5 2(5+1) 2(3+1) +1
7 3(7+1) 3(7+1) +1
9 4(9+1) 4(9+1) +1

SO, the triplets are:

( n; nsq-1/2 ; nsq +1/2)

when n is odd n is (3,5,7,....)
*********

2.

3. Awesome, sorry I didn't get back to you. I've been busy the past two days and have had guests over. Nice work!

4. it's great that u like it ,..actully i was not close to my friend's solution, i like this answer,..seems like numbers game,..
(donnt carre about being late )
thx for ure reply

Silex7

5. Maybe its just me, but the formula doesnt work for me. For instance n=3:

(3, 3sq-1/2, 3sq+1/2) = (3, 8.5, 9.5)

Not a Pythagorean triplet!

6.

7. That helps quite a bit! But even the forula they give doesnt give us ALL pythagorean triples that your professor wanted.

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