The application of a new mean value theorem to the fractional parts
... advances in Waring’s problem (see, in particular, [9, 10, 11, 14]) may plainly be applied to improve current estimates for kαnk k, the distance from αnk to the nearest integer (which is intimately related to the fractional part of αnk ). The rather recent arrival of these new estimates has apparentl ...
... advances in Waring’s problem (see, in particular, [9, 10, 11, 14]) may plainly be applied to improve current estimates for kαnk k, the distance from αnk to the nearest integer (which is intimately related to the fractional part of αnk ). The rather recent arrival of these new estimates has apparentl ...
Grade 6 Math Circles Sequences What is a Sequence?
... between the two is that while sets are unordered, the order of a sequence does matter. In fact, the order of the sequence is what defines its rule. The best way to explain this is through an example: When we take the set of positive even numbers less than 10, we can write {2,4,6,8} or {4,8,2,6} - th ...
... between the two is that while sets are unordered, the order of a sequence does matter. In fact, the order of the sequence is what defines its rule. The best way to explain this is through an example: When we take the set of positive even numbers less than 10, we can write {2,4,6,8} or {4,8,2,6} - th ...
Full text
... nonunitary aliquot sequences exist is an open question. An investigation was made of all nonunitary aliquot sequences with leader n < 1 0 6 . About 40 minutes of computer time was required. 740671 sequences were found to be terminating; 1440 were periodic (194 ended in 1-cycles, 1195 in 2-cycles, an ...
... nonunitary aliquot sequences exist is an open question. An investigation was made of all nonunitary aliquot sequences with leader n < 1 0 6 . About 40 minutes of computer time was required. 740671 sequences were found to be terminating; 1440 were periodic (194 ended in 1-cycles, 1195 in 2-cycles, an ...
Limits of sequences
... Limits of sequences mc-TY-sequences-2009-1 In this unit, we recall what is meant by a simple sequence, and introduce infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequence ...
... Limits of sequences mc-TY-sequences-2009-1 In this unit, we recall what is meant by a simple sequence, and introduce infinite sequences. We explain what it means for two sequences to be the same, and what is meant by the n-th term of a sequence. We also investigate the behaviour of infinite sequence ...
Entering Algebra I Worksheet
... This summer math worksheet is for all students entering a high school level Algebra 1 class. Work the following problems over the summer. Be sure to show ALL your work neatly on a separate sheet of paper. Your teacher will ask for this in August for a grade. NO Calculators should be used on this wor ...
... This summer math worksheet is for all students entering a high school level Algebra 1 class. Work the following problems over the summer. Be sure to show ALL your work neatly on a separate sheet of paper. Your teacher will ask for this in August for a grade. NO Calculators should be used on this wor ...
Full text
... of the s(n) representations of n as a difference of squares from the factorizations ab~n with a>b>0 and a = ±b (mod 2), using (x9y) = (j2f^3 - ^ . To illustrate this, we shall calculate the representations in the case of a square and nonsquare number. Beginning with, say n = 22 -5-7, we have that d^ ...
... of the s(n) representations of n as a difference of squares from the factorizations ab~n with a>b>0 and a = ±b (mod 2), using (x9y) = (j2f^3 - ^ . To illustrate this, we shall calculate the representations in the case of a square and nonsquare number. Beginning with, say n = 22 -5-7, we have that d^ ...
Full text
... m = 2, there corresponds one representation calculated via (2) with n = ((2 • 5 • 7)2 -1) / 2. Apart from (c, J ) = (5-7,5-7), all of the factorizations (c9d) e{(5,5-7 2 ),(5 2 , 7 2 ),(5 2 -7, 7)} will each produce two distinct representations via (3) and (4). However, for (c, d) - (5- 7,5* 7), the ...
... m = 2, there corresponds one representation calculated via (2) with n = ((2 • 5 • 7)2 -1) / 2. Apart from (c, J ) = (5-7,5-7), all of the factorizations (c9d) e{(5,5-7 2 ),(5 2 , 7 2 ),(5 2 -7, 7)} will each produce two distinct representations via (3) and (4). However, for (c, d) - (5- 7,5* 7), the ...
