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 3
... common difference of which is 1 ; thus , Arith . series , 1 2 3 4 Triangular } B 2 Definitions . 3.
... common difference of which is 1 ; thus , Arith . series , 1 2 3 4 Triangular } B 2 Definitions . 3.
Σελίδα 4
... common difference of which is 2 ; thus , Arith . series , Quadrang , or square numb . 1 3 5 7 9 11 , & c . 1 4 9 16 25 36 , & c . 25. Pentagonal Numbers , are the sums of an arithmetical series , beginning with unity , the com- mon ...
... common difference of which is 2 ; thus , Arith . series , Quadrang , or square numb . 1 3 5 7 9 11 , & c . 1 4 9 16 25 36 , & c . 25. Pentagonal Numbers , are the sums of an arithmetical series , beginning with unity , the com- mon ...
Σελίδα 11
... common divisor ( prop . vi . ) ; that is , a and b would have a common measure , which is contrary to the ... difference ( a - b ) is prime to each of them , if ( a - b ) > 1 . Cor . 2. If a number , consisting of two parts , as ( a + b ) ...
... common divisor ( prop . vi . ) ; that is , a and b would have a common measure , which is contrary to the ... difference ( a - b ) is prime to each of them , if ( a - b ) > 1 . Cor . 2. If a number , consisting of two parts , as ( a + b ) ...
Σελίδα 12
... difference of those numbers ( a + b ) is divisible by p . Cor . 4. If a number , consisting of many parts , have all ... common measure 2 . For if ( a + b ) , and ( a - b ) , have any common measure , their sum and difference , 2a and 2b ...
... difference of those numbers ( a + b ) is divisible by p . Cor . 4. If a number , consisting of many parts , have all ... common measure 2 . For if ( a + b ) , and ( a - b ) , have any common measure , their sum and difference , 2a and 2b ...
Σελίδα 19
... difference of two fractions , which are in their lowest terms , and of which the denominator of the one contains a factor not common with the other , can be equal to an in- teger number . Let- , and Α ́ b Bt be any two fractions in ...
... difference of two fractions , which are in their lowest terms , and of which the denominator of the one contains a factor not common with the other , can be equal to an in- teger number . Let- , and Α ́ b Bt be any two fractions in ...
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An Elementary Investigation of the Theory of Numbers: With Its Application ... Peter Barlow Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
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4th power answer the required aq² arithmetical progression ascertain assuming ax² Ay² bx² 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 foregoing proposition form 4n form 4n+1 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