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From: M. M i c h a e l M u s a t o v on 1 Feb 2010 22:43 On Feb 1, 5:21 pm, master1729 <tommy1...(a)gmail.com> wrote: > alainverghote wrote : > > > > > > > On 1 fév, 00:17, master1729 <tommy1...(a)gmail.com> > > wrote: > > > alain wrote : > > > > > On 30 jan, 21:40, master1729 > > <tommy1...(a)gmail.com> > > > > wrote: > > > > > i wrote : > > > > > > > alainverghote wrote : > > > > > > > > Good morning, > > > > > > > > I just wish to propose you the following > > > > equality: > > > > > > > > (11a+14c)*(12a+13c)*(13a+12c)*(14a+11c) > > > > > > > = > > > > > > > [155(a^2+c^2)+315ac]^2 - (a-c)^4 > > > > > > > > Of course there must be some nice > > 'extensions' > > > > of > > > > > > it! > > > > > > > > Alain > > > > > > > the trend would probably be > > > (10a+15c)*(11a+14c)*(12a+13c)*(13a+12c)*(14a+11c)*(15a > > > > > > +10c) > > > > > > > = ... > > > > > > > one can work that out but im not sure if its > > a > > > > nice > > > > > > extension or one that you like. > > > > > > > i guess it isnt a difference of squares but i > > > > havent > > > > > > checked yet. > > > > > > > im not sure what you are looking for but i > > like > > > > it > > > > > > :) > > > > > > > sometimes i like vague ideas. > > > > > > > ( i think many do not because it differs > > strongly > > > > > > from definitions and proofs ) > > > > > > > i think it might be usefull to replace a with > > 2 > > > > and > > > > > > consider falling and rising factorials that > > are > > > > > > differences of 2 squares and then see if we > > can > > > > > > replace the 2 with a again and still have the > > > > > > difference of 2 squares. > > > > > > > i think what you are looking for are > > properties > > > > of a > > > > > > kind of factorial-like function. > > > > > > > regards > > > > > > > tommy1729 > > > (9a+16c)*(10a+15c)*(11a+14c)*(12a+13c)*(13a+12c)*(14a+ > > > > 11c)*(15a+10c)*(16a+9c) > > > > > = ... > > > > > > also seems intresting ... or not ?- Masquer le > > > > texte des messages précédents - > > > > > > - Afficher le texte des messages précédents - > > > > > Bonjour Tommy, > > > > > What often matters is to get out the underlying > > > > structure > > > > of a messy cumbersome polynomial writing, > > > > Your case with t = a-c , u = 9a+16c > > > > nicely simplifies: > > > > u(u+t)(u+2t)(u+3t)(u+4t)(u+5t)(u+6t)(u+7t) > > (1) > > > > More we've got: > > > > [(u+t)(u+6t)][(u+2t)(u+5t)] = (u^2+7ut+8t^2)^2 > > -4t^4 > > > > [u(u+t)(u+7t)][(u+3t)(u+4t)] = > > (u^2+7ut+6t^2)^2-36t^4 > > > > > Or the form of product (1) may be considered as > > : > > > > (ac)^2+(bd)^2 - [(ad)^2+(bd)^2] > > > > > Amicalement, > > > > Alain > > > > so , was that what you are looking for ? > > > > how does the generalization look like ?- Masquer le > > texte des messages précédents - > > > > - Afficher le texte des messages précédents - > > > Good morning dear Master, > > > Well, I still do not know... > > > Alain > > well what fascinates me is the relationship to the gamma function. > > i wonder if its also possible to arrive at an analogue of the form a^2 + b^2 instead of a^2 - b^2 , mainly because of factorizations into primes of the form x^2 + y^2. > > i think so , perhaps replace c with 4c or 4c + 1 or so ... > > regards > > tommy1729- Hide quoted text - > > - Show quoted text - AUTO-MEAMI-ORG RESPONSE: Results 651 - 654 for (16a+9c). (0. 45 seconds) Crystal structure of the product of a condensation reaction of . .. .. by M Gdaniec - 1994 - Related articles C(16A) 7276(4) -1135(11) 9247(3) 53(3). C(17A) 6961(4) 153(10) 9375(3) 52(3) . .. .. .. .. C(7)-O(3) 1. 272(11) 1. 281(9) C(17)-O(7) 1. 279(9) 1. 292(9) . .. .. www. springerlink. com/index/PG521L760204442R. Supramolecular framework adducts constructed of . .. .. by F Xue - 1996 - Related articles Na(I)--N(16A). Na(1)-- N(23C). Fe(I)--C(I 1). Fe(I)--C(12). Fe(I)--C(13) . .. .. .. 1490(9) " C(35)--N(32). 1. 474(8). C(35)--N(34). 1473(9). C(36)--N(33) . .. .. www. springerlink. com/index/YV673334500457U2. Reactions of dibenzylphosphine oxide with α,β . .. .. by VD Kolesnik - 2002 - Related articles (dd, 1 H, H(16a), J = 14. 5 Hz, J = 14. 3 Hz); 3. 20 (dd, 1 H . .. .. 128. 08, 128. 16, and 128. 42 (C(8), C(9), C(10), C(11)); 129. 66. (Cm/p, JCP = 4. 7 Hz); . .. .. www. springerlink. com/index/34D9WXP58HBAQLJR. Structure of cis-4-hydroxy-N-triphenylmethyl-l-proline methyl esterby G Stavropoulos - 1990 - Related articles C(16A). 11277 (3). 5365 (5). 7346 (3). 5-16 (16). C(17A). 11548 (3). 6080 (5) . .. .. .. C(9)--C(10). 1-386 (6). 1. 413 (6). C(25)--O(26) 1. 300 (6). 1. 356 (6) . .. .. journals. iucr. org/c/issues/1990/08/00/mu0107/mu0107. Previous 56 57 58 59 60 61 62 63 64 65 66 http://www. meami. org/?cx=000961116824240632825%3A5n3yth9xwbo&cof=FORID%3A9%3B+NB %3A1&ie=UTF-8&q=(16a%2B9%C2%ADc)+#480 |