The Collected Mathematical Papers of Arthur Cayley volume 4
The Collected Mathematical Papers of Arthur Cayley volume 4
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In our eReader you can find the full English version of the book. Read The Collected Mathematical Papers of Arthur Cayley volume 4 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Collected Mathematical Papers of Arthur Cayley volume 4
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But in this case K is of the same species with K, viz. , of the species I. , and by the theorem, K (X, Y) = (6* X, W F) where of = d (c + d ) -l, ij = a (a -b )-l (mod. 16) ; and we ought to have that is a/ = r, y = y (mod. 16), d (c + d )-l=d(c + d)-I+r, (mod. 16), or substituting for a, b, c, d their values a + br, b, c + dr, d, these become d(c + d + dr) = d (c + d) + r, (mod. 16), (a + br) (a b + br) = a(a b) or (mod. 16).
293] ON A CEKTAIN SYSTEM OF FUNCTIONAL SYMBOLS. 489 But r being even..., these become d 2 - 1 = 0, 2ab - b" + b*r = (mod. 8) ; or, since in the case under consideration, a, b, c, d = 1, 0, 0, 1 (mod. 2), and therefore 6 2 r = (mod. 8), the two congruences become d? - 1 = 0, a 2 - (a - 6) 2 = (mod. 8), which are satisfied since d, a, and a b are all odd. And in a similar way the theorem is proved for all the other cases.
In M. Hermite s problem, X, Y are replaced by, ^u>, AX, AY are (w + l). I/r(o) + l), and EX, BY are $( --, ^( --, the properties of the functions , ^ being such that, as in the preceding investigation, A(X, F)=0, , B(X, F) = (F, X), where 0(=e i!r ) is a sixteenth root of unity, and KX, KY are respectively equal to ( rZ"^J ^ (, ?
What to read after The Collected Mathematical Papers of Arthur Cayley volume 4?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Cayley to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
But in this case K is of the same species with K, viz. , of the species I. , and by the theorem, K (X, Y) = (6* X, W F) where of = d (c + d ) -l, ij = a (a -b )-l (mod. 16) ; and we ought to have that is a/ = r, y = y (mod. 16), d (c + d )-l=d(c + d)-I+r, (mod. 16), or substituting for a, b, c, d their values a + br, b, c + dr, d, these become d(c + d + dr) = d (c + d) + r, (mod. 16), (a + br) (a b + br) = a(a b) or (mod. 16).
293] ON A CEKTAIN SYSTEM OF FUNCTIONAL SYMBOLS. 489 But r being even..., these become d 2 - 1 = 0, 2ab - b" + b*r = (mod. 8) ; or, since in the case under consideration, a, b, c, d = 1, 0, 0, 1 (mod. 2), and therefore 6 2 r = (mod. 8), the two congruences become d? - 1 = 0, a 2 - (a - 6) 2 = (mod. 8), which are satisfied since d, a, and a b are all odd. And in a similar way the theorem is proved for all the other cases.
In M. Hermite s problem, X, Y are replaced by
What to read after The Collected Mathematical Papers of Arthur Cayley volume 4?
You can find similar books in the "Read Also" column, or choose other free books by Arthur Cayley to read onlineMoreLess
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