Problem with determining squareroots in the progressions.. - Page 4

wblipp · 2003-07-24, 14:46

Quote:

Originally Posted by Annunaki

hmm.. i will look at it a little bit later.. but for now it seems that it may be something good.. Hovewer we need to find a way to include 0th element..
and in general case i need only to find soonest square not all of them.. but of course this mehod still looks good for now..

I don't see a way to include an arbitrary zeroth element into this approach - is there perhaps some relationship between your zeroth element and your initial element we could exploit?

I haven't thought too much about the "soonest" issue, but because f = 2a-1 and a = d*(p^2+q^2), it should be easy to select the values of d, p, and q that give the smallest a and therefor the smallest f.

Annunaki · 2003-07-24, 18:23

i fear there are no more relationship between oth elment and first element.. the only thing I can say about 0th element that it will be allways at least by 3 lesser than fisrt element.. thus the 0th<1st-2
I think the only way to include 0th element is to find a squence that has exactly the same number of elements, but the sum is allways largen than that of the orginal sequenece by 0th element
for example if:
sequence is
8, 21, 23, 25 ,27
we can shiwtch it to 23,25,27,29..
but that is only in casw with 4 elements but i still think that it can be done..
only i still cant figure how..

Annunaki · 2003-07-24, 19:13

may be a proof to hte statement that every Pythagoreon triple can be formed from natural p and q if sides are - 2pq; p^2+q^2; p^2-q^2; could help us..
thus may be if we know on what is based this statement we can step a little bit higher..

Annunaki · 2003-07-26, 15:00

hmm i think i noticed something..
and i can include 0th element..
can you check easely when some triple will be Pythagoreon triple..
for example
if i know two sides of that triple.. and they grow in progression..
Can i know when natural Pythagoreon triple will be posible for example i know.. that
two sides of triple are
26; 25
28; 25
30; 25
etc.. can i tell when triple of Pythagorian will be possible.. According to what i can read it is posible even very posible.. but that is too easy.. that is why I can`t believe in that.. I will think about it again..

Annunaki · 2003-07-26, 15:19

hmh .. i think i found a bug in my previous post..
that is not so easy..
i dont need to find only when it will be Pythagoreon triple..
i Actually need to know if pythagoreon triple would be posible if I add 0th element:(
in that case it would be.. 0th=14
26^2-25^2 +14
28^2-25^2 +14
30^2-25^2 +14
etc. notice that 30^2-25^2+14 gives us answer as it is 289=17^2..
but can we tell it somehow more efectively..

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2003-07-24, 18:23	#35
Annunaki Jul 2003 1F₁₆ Posts	i fear there are no more relationship between oth elment and first element.. the only thing I can say about 0th element that it will be allways at least by 3 lesser than fisrt element.. thus the 0th<1st-2 I think the only way to include 0th element is to find a squence that has exactly the same number of elements, but the sum is allways largen than that of the orginal sequenece by 0th element for example if: sequence is 8, 21, 23, 25 ,27 we can shiwtch it to 23,25,27,29.. but that is only in casw with 4 elements but i still think that it can be done.. only i still cant figure how..

2003-07-24, 19:13	#36
Annunaki Jul 2003 31 Posts	may be a proof to hte statement that every Pythagoreon triple can be formed from natural p and q if sides are - 2pq; p^2+q^2; p^2-q^2; could help us.. thus may be if we know on what is based this statement we can step a little bit higher..

2003-07-26, 15:00	#37
Annunaki Jul 2003 31 Posts	hmm i think i noticed something.. and i can include 0th element.. can you check easely when some triple will be Pythagoreon triple.. for example if i know two sides of that triple.. and they grow in progression.. Can i know when natural Pythagoreon triple will be posible for example i know.. that two sides of triple are 26; 25 28; 25 30; 25 etc.. can i tell when triple of Pythagorian will be possible.. According to what i can read it is posible even very posible.. but that is too easy.. that is why I can`t believe in that.. I will think about it again..

2003-07-26, 15:19	#38
Annunaki Jul 2003 31 Posts	hmh .. i think i found a bug in my previous post.. that is not so easy.. i dont need to find only when it will be Pythagoreon triple.. i Actually need to know if pythagoreon triple would be posible if I add 0th element:( in that case it would be.. 0th=14 26^2-25^2 +14 28^2-25^2 +14 30^2-25^2 +14 etc. notice that 30^2-25^2+14 gives us answer as it is 289=17^2.. but can we tell it somehow more efectively..