An Elementary Investigation of the Theory of Numbers: With Its Application to the Indeterminate and Diophantine Analysis, the Analytical and Geometrical Division of the Circle, and Several Other Curious Algebraical and Arithmetical ProblemsJ. Johnson, 1811 - 507 σελίδες |
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Σελίδα vii
... least unimproved , till Bachet , a French analyst of considerable reputation , undertook the translation of the abovementioned work into Latin , retaining also the Greek text , which was published by him in 1621 , interspersed with many ...
... least unimproved , till Bachet , a French analyst of considerable reputation , undertook the translation of the abovementioned work into Latin , retaining also the Greek text , which was published by him in 1621 , interspersed with many ...
Σελίδα xiv
... of the Circle Table of Prime Numbers to 4000 Table containing the least Falues of p and q in the Equation p2 - Nq = 1 , for every Value of x , from 2 to 102 · 479 506 . 507 ERRATA . Page 20 , line 2 , for " Siv CONTENTS .
... of the Circle Table of Prime Numbers to 4000 Table containing the least Falues of p and q in the Equation p2 - Nq = 1 , for every Value of x , from 2 to 102 · 479 506 . 507 ERRATA . Page 20 , line 2 , for " Siv CONTENTS .
Σελίδα 15
... least of all those numbers that are prime to p , and that renders the product ab divisible by p . Now since b is prime to p , we may make p = nb + b ' , in which formula , b ' < b , and also prime to both p and b ( prop . x . ) ; also b ...
... least of all those numbers that are prime to p , and that renders the product ab divisible by p . Now since b is prime to p , we may make p = nb + b ' , in which formula , b ' < b , and also prime to both p and b ( prop . x . ) ; also b ...
Σελίδα 16
... least of all those , that render the product ab divisible by p ; but if there were any such numbers , one of them must necessarily be the least ; therefore , there are no such numbers ; and , consequently , if p be prime to two other ...
... least of all those , that render the product ab divisible by p ; but if there were any such numbers , one of them must necessarily be the least ; therefore , there are no such numbers ; and , consequently , if p be prime to two other ...
Σελίδα 21
... , as c ' ; and so on , as long as division . can be made , so shall we have p = a " b TM c2 , & c . Q. E. D. Cor . 1. From the foregoing proposition it ap- pears , that the least divisor of every number is Numbers in General . 21.
... , as c ' ; and so on , as long as division . can be made , so shall we have p = a " b TM c2 , & c . Q. E. D. Cor . 1. From the foregoing proposition it ap- pears , that the least divisor of every number is Numbers in General . 21.
Άλλες εκδόσεις - Προβολή όλων
An Elementary Investigation of the Theory of Numbers: With Its Application ... Peter Barlow Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
4th powers answer the required arithmetical progression ascertain assuming Ay² becomes bx² by² coefficients common difference common divisor common measure complete quotient consequently contained continued fraction converging fractions cx² deduced demonstrated denary denominator digits divided divisible equa equal equation x² evident expression factors find the values fore foregoing proposition form 4n+1 forms 4n formula given number gives hence impossible form indeterminate equation integer number least number modulus multiplication Nq² number of solutions numbers in arithmetical numbers prime Ny² obtain odd number periods prime number PROP proposed equation Q. E. D. Cor quantities radix rational represent required conditions Required the value resolved Scholium square numbers substituting suppose theorem tion transformed unity values of x whence x²² y²²
Δημοφιλή αποσπάσματα
Σελίδα 43 - Euler ascertained, that 231 — 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers, which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it.
Σελίδα 477 - Find two numbers whose" product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.
Σελίδα 84 - If a square number terminate with an odd digit, the last figure but one will be even ; and if it terminate with any even digit, except 4, the last figure but one will be odd. 27. No square number can terminate with two equal digits, except two ciphers or two fours, 28.
Σελίδα 23 - ... if a square number be either multiplied or divided by a number that is not a square, the product or quotient is not a square.
Σελίδα 7 - The sum or difference of two odd numbers, is even ; but the sum of three odd numbers, is odd. 4. The sum of any even number of odd numbers, is even ; but the sum of any odd number of odd numbers, is odd. 5. The sum, or difference, of an even and an odd number, is an odd number.
Σελίδα 1 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Σελίδα 216 - I have been the first to discover a most beautiful theorem of the greatest generality, namely this: Every number is either a triangular number or the sum of two or three triangular numbers; every number is a square or the sum of two, three, or four squares...
Σελίδα 83 - If a square number terminate with a 4, the last figure but one (towards the right hand) will be an even number. 25. If a square number terminate with 5, it will terminate with 25. 26. If a square number terminate with an odd digit, the last figure but one will be even ; and if it terminate with any even digit, except 4, the last figure but one will be odd. 27.
Σελίδα 19 - If an odd number divides an even number, it will also divide the half of it 11. If a number consist of many parts, and each of those parts have a common divisor d, then will the whole number, taken collectively, be divisible by d. 12. Neither the sum nor the difference of two fractions, which are in their lowest terms, and of which the denominator of the one contains a factor not common to the other, can be equal to an integer number.