A note on A007775
... where qs (n) is a polynomial in n with rational coe cients. Computer calculation shows that in fact qs (n) has integer coe cients for each of the sixteen values of s between 1 and 60 not divisible by 2, 3 or 5. It follows from is (2) that for these sixteen values of s the expression n(n+s)(n+2s)(n+3 ...
... where qs (n) is a polynomial in n with rational coe cients. Computer calculation shows that in fact qs (n) has integer coe cients for each of the sixteen values of s between 1 and 60 not divisible by 2, 3 or 5. It follows from is (2) that for these sixteen values of s the expression n(n+s)(n+2s)(n+3 ...
Cn2 - ITWS
... Raising Raise Fraction: Multiply N & D by needed number! Multiply T & B by same number is Fair! Raise to 6ths: 2/3 = (2x2) / (3x2) = 4/6 Raise to 15ths: 4/5 = (4x3) / (5x3) = 12/15 Raise to 10ths: 1/2 = (1x5) / (2x5) = 5/10 Raising fractions is used in combining like Fractions! ...
... Raising Raise Fraction: Multiply N & D by needed number! Multiply T & B by same number is Fair! Raise to 6ths: 2/3 = (2x2) / (3x2) = 4/6 Raise to 15ths: 4/5 = (4x3) / (5x3) = 12/15 Raise to 10ths: 1/2 = (1x5) / (2x5) = 5/10 Raising fractions is used in combining like Fractions! ...
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... You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
Positive and Negative Numbers
... Problem 2 • Pete chose several positive and negative points on the coordinate line. Mary added all these numbers together and got 25. Pete moved all points by 5 units to the left. Mary added the new numbers together and got –35. ...
... Problem 2 • Pete chose several positive and negative points on the coordinate line. Mary added all these numbers together and got 25. Pete moved all points by 5 units to the left. Mary added the new numbers together and got –35. ...
NUMBER SYS LEC -1
... If we include zero (0) to collection of natural numbers, then all together from whole numbers Whole numbers W = {0} + N ...
... If we include zero (0) to collection of natural numbers, then all together from whole numbers Whole numbers W = {0} + N ...
to get a 5 (30 ÷ 6) 5 times.
... 23. In the sequence: 1, 8, 15, 22, 29, … 113, each term is 7 more than the preceding term. We can say that 1 + 7 x ? = 113. The value of the ? is given by (113 - 1) ÷ 7. This value is 16. In this sequence, there are (16 + 1) 17 terms. 24. When he stops, after having covered 70% of the distance, Math ...
... 23. In the sequence: 1, 8, 15, 22, 29, … 113, each term is 7 more than the preceding term. We can say that 1 + 7 x ? = 113. The value of the ? is given by (113 - 1) ÷ 7. This value is 16. In this sequence, there are (16 + 1) 17 terms. 24. When he stops, after having covered 70% of the distance, Math ...
Automata and Rational Numbers - the David R. Cheriton School of
... numbers in the “middle-thirds” Cantor set with denominators a power of 3. Example 4. Let k = 2, and consider L4 := [0, 1]{[0, 0], [0, 1]}∗ {[1, 0], [1, 1]}. Then the numerator encodes the integer 1, while the denominator encodes all positive integers that start with 1. Hence quok (L4 ) = { ...
... numbers in the “middle-thirds” Cantor set with denominators a power of 3. Example 4. Let k = 2, and consider L4 := [0, 1]{[0, 0], [0, 1]}∗ {[1, 0], [1, 1]}. Then the numerator encodes the integer 1, while the denominator encodes all positive integers that start with 1. Hence quok (L4 ) = { ...
Full text
... The validity of (3.3) follows necessarily from (3.5) and (3.4). • An Observation: At first sight, we were amazed at the relatively large number of prime Mn (cf. Sequences 179 and 1558 of [4]): we found 48 of them for 3
... The validity of (3.3) follows necessarily from (3.5) and (3.4). • An Observation: At first sight, we were amazed at the relatively large number of prime Mn (cf. Sequences 179 and 1558 of [4]): we found 48 of them for 3
Three Connections to Continued Fractions
... Where can I find out more about continued fractions? Most elementary number theory books have chapters devoted to continued fractions. See, for example, [6] (a classic), [7] (which also treats generalized continued fractions), [8] and [12]. Olds’ book [10] is a very nice elementary introduction. Per ...
... Where can I find out more about continued fractions? Most elementary number theory books have chapters devoted to continued fractions. See, for example, [6] (a classic), [7] (which also treats generalized continued fractions), [8] and [12]. Olds’ book [10] is a very nice elementary introduction. Per ...
Solutions 2
... which means that only integers can be represented by Cauchy sequences of integers. (+10) *c) Suppose {xk } = x1 , x2 , x3 , ... and {yk } = y1 , y2 , y3 , ... are two sequences of rational numbers. Define the shuffled sequence to be x1 , y1 , x2 , y2 , x3 , y3 , .... Prove that the shuffled sequence ...
... which means that only integers can be represented by Cauchy sequences of integers. (+10) *c) Suppose {xk } = x1 , x2 , x3 , ... and {yk } = y1 , y2 , y3 , ... are two sequences of rational numbers. Define the shuffled sequence to be x1 , y1 , x2 , y2 , x3 , y3 , .... Prove that the shuffled sequence ...
