A Survey on Triangular Number, Factorial and Some Associated
... properties8. Many other important results on these numbers have been discussed in the literature. A theorem of Fermat states that a positive integer can be expressed as a sum of at most three triangular, four square, five pentagonal, or n n-gonal numbers. Gauss proved the triangular case10,15. Euler ...
... properties8. Many other important results on these numbers have been discussed in the literature. A theorem of Fermat states that a positive integer can be expressed as a sum of at most three triangular, four square, five pentagonal, or n n-gonal numbers. Gauss proved the triangular case10,15. Euler ...
Full text
... computer at Los Alamos he is able to generate displays having around 65,000 points in them. It would be of interest to try something of the same sort for the Fibonacci, Lucas, and other recurrent sequences, however the writer does not have available such versatile equipment as that used by Ulam and ...
... computer at Los Alamos he is able to generate displays having around 65,000 points in them. It would be of interest to try something of the same sort for the Fibonacci, Lucas, and other recurrent sequences, however the writer does not have available such versatile equipment as that used by Ulam and ...
Reverse Mathematics and the Coloring Number of Graphs
... compactness) asserts the existence of sets definable by formulas that only quantify over number variables. ATR0 (Arithmetic Transfinite Recursion) is equivalent to any two countable well orders being comparable, while Π11 -CA0 asserts the existence of Π11 sets. A Π11 set is one that is definable by ...
... compactness) asserts the existence of sets definable by formulas that only quantify over number variables. ATR0 (Arithmetic Transfinite Recursion) is equivalent to any two countable well orders being comparable, while Π11 -CA0 asserts the existence of Π11 sets. A Π11 set is one that is definable by ...
Number Operations and Integers
... NOT: /A/Is this a multiple of the least number? If so, check to see whether there is a lesser multiple common to all three of the numbers. /B/Correct! /C/Is this a multiple of the greatest number? If so, check to see whether there is a lesser multiple common to all three./D/Check to be sure this is ...
... NOT: /A/Is this a multiple of the least number? If so, check to see whether there is a lesser multiple common to all three of the numbers. /B/Correct! /C/Is this a multiple of the greatest number? If so, check to see whether there is a lesser multiple common to all three./D/Check to be sure this is ...
19(2)
... 2, ..., n}, {^i,J- + £ , k + £ : • & = l', 2,'..., n} and {ai + £, J.+ £sfc+£: £*=' 1, 2, ..., n] constitute the diagonals. Note that a diagonal is either broken or unbroken; being unbroken if all n of its elements lie on a straight line. The unbroken diagonals consist of the main diagonals, of whic ...
... 2, ..., n}, {^i,J- + £ , k + £ : • & = l', 2,'..., n} and {ai + £, J.+ £sfc+£: £*=' 1, 2, ..., n] constitute the diagonals. Note that a diagonal is either broken or unbroken; being unbroken if all n of its elements lie on a straight line. The unbroken diagonals consist of the main diagonals, of whic ...
Shape is a Non-Quantifiable Physical Dimension
... the hyperbolas; let us associate all these parabola curvatures with the number 1, since they have the same eccentricity, 1. Third, let us look at the curvatures at the end points of the major axis of the ellipses. They differ from that of the hyperbolas and parabolas, and they also differ from each ...
... the hyperbolas; let us associate all these parabola curvatures with the number 1, since they have the same eccentricity, 1. Third, let us look at the curvatures at the end points of the major axis of the ellipses. They differ from that of the hyperbolas and parabolas, and they also differ from each ...
40(3)
... 3. THE BURGSTAHLER PROBLEM AS AN INVERSION PROBLEM The real problem considered in this paper is the following: Find the sequence 62n+1 given that u ...
... 3. THE BURGSTAHLER PROBLEM AS AN INVERSION PROBLEM The real problem considered in this paper is the following: Find the sequence 62n+1 given that u ...
I. Sequence
... Thm 4 allows us to use L’Hopital’s Rule to find limits of some sequences. D. Examples: Do the following sequences converge? ...
... Thm 4 allows us to use L’Hopital’s Rule to find limits of some sequences. D. Examples: Do the following sequences converge? ...
