This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1907 Excerpt: ...norm q, ....i....rn are primary prime tettarions of norm t, all being of the form 286. Definition. An integral tettarion is primitive if its coordinates have no common divisor other than unity. It is primitive to an integer m when its coordinates are all prime to m. Every primary tettarion is also primitive. 287. Theorem. Let y be a primitive integral tettarion and N(y)=paiqat f where p, q....t are the prime factors of N (y). Then y can be decomposed in only one way into the form y = n1 nxi, Tj . e where e is a unit tettarion, and n1 nai are prime tettarions of norm p, i o, are prime tettarions of norm q, rt Tfc are prime tettarions of norm t. The product of each I successive factors is primary, where I = 1.... a (i = 1 n) 288. Definition. If al) a2 a, are s integral tettarions of equal norms JV(ai) = N(a2) = N(a, ), and if a1 a2... a, =-W(aj), then these tettarions are semi-conjugate. 289. Theorem. A product of any number of prime tettarions of forms 2dueii is a primitive tettarion of the same form if among the factors no s of them are semi-conjugate. 290. Theorem. A product of primary prime tettarions iti nn, where N(ni) =Pi (-=l....n) Pi being distinct primes, is always a primitive tettarion. 291. Definition. Two given tettarions a and (3 are pre-(post-) congruent to a modulus y, if their difference a--/? is pre-(post-) divisible by y. This congruence is indicated by a = /? (mod y, pre) or a = j3 (mod y, post) There is then an integral tettarion such that a--(3 = y'C, or %y 292. Theorem. If a and (3 are pre-(post-) congruent modulo y, they are also pre-(post-) congruent for any tettarion post-(pre-) associated with y, as modulus. 293. Theorems. If a = r (J = r then a = /3 (mod y) If a = r /? = a then a /? = r cr (mod y) ...