Transcendental values of the digamma function
... We hasten to point out that theorems similar to Theorems 9 and 10 have been proved in [1]. In a related context, Erdős (see [8]) conjectured that there is no function defined on the integers with period q satisfying f (q) = 0, f (a) = ±1 for 1 a q − 1 such that ...
... We hasten to point out that theorems similar to Theorems 9 and 10 have been proved in [1]. In a related context, Erdős (see [8]) conjectured that there is no function defined on the integers with period q satisfying f (q) = 0, f (a) = ±1 for 1 a q − 1 such that ...
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... A Hurwitz integer is defined to be a Hurwitz prime if its H-norm is a prime number p Z. Note that the norm on H restricts to a Z-valued function on the set of Hurwitz integers. Therefore the definition of a Hurwitz prime makes sense, and is completely analogous to Z[i]. Remark 3.6. The correct def ...
... A Hurwitz integer is defined to be a Hurwitz prime if its H-norm is a prime number p Z. Note that the norm on H restricts to a Z-valued function on the set of Hurwitz integers. Therefore the definition of a Hurwitz prime makes sense, and is completely analogous to Z[i]. Remark 3.6. The correct def ...
2.1 Introduction to Fractions and Mixed Numbers
... 1. Identify numerator and denominator of a fraction. Review division properties of 0 and 1. 2. Write a fraction to represent the shaded part of a figure. 3. Identify proper fractions, improper fractions, and mixed numbers. 4. Write mixed numbers as improper fractions. 5. Write improp ...
... 1. Identify numerator and denominator of a fraction. Review division properties of 0 and 1. 2. Write a fraction to represent the shaded part of a figure. 3. Identify proper fractions, improper fractions, and mixed numbers. 4. Write mixed numbers as improper fractions. 5. Write improp ...
Necessary Conditions For the Non-existence of Odd Perfect Numbers
... B2 = 2 with the rest of the Bi ’s equal to 1, then N is not OP. Also, Kanold showed that if e = 5, and the Bi ’s are any combination of 1’s or 2’s, then N is not OP ([KAN2]). This historical section will end with a new proof of the nonexistence of OP numbers of the form N = q e ∗ a21 ∗ ... ∗ a2n . ...
... B2 = 2 with the rest of the Bi ’s equal to 1, then N is not OP. Also, Kanold showed that if e = 5, and the Bi ’s are any combination of 1’s or 2’s, then N is not OP ([KAN2]). This historical section will end with a new proof of the nonexistence of OP numbers of the form N = q e ∗ a21 ∗ ... ∗ a2n . ...
Asymptotically Lacunary Statistical Equivalent Sequences of Fuzzy
... Bol. Soc. Paran. Mat. c SPM –ISSN-2175-1188 on line SPM: www.spm.uem.br/bspm ...
... Bol. Soc. Paran. Mat. c SPM –ISSN-2175-1188 on line SPM: www.spm.uem.br/bspm ...
unit 1 fractions. rational numbers. - Over-blog
... 1) Terminating decimals: decimal numbers with a fixed number of decimal places. To get the fraction form, put in the numerator all the digits of the number −without the decimal point−, and the denominator is 1 followed by as many zeros as decimal places has the number. Simplify if possible. ...
... 1) Terminating decimals: decimal numbers with a fixed number of decimal places. To get the fraction form, put in the numerator all the digits of the number −without the decimal point−, and the denominator is 1 followed by as many zeros as decimal places has the number. Simplify if possible. ...
Generalized Sierpinski numbers base b.
... ‡ Just those smaller than conjectured least base b Sierpiński and with gcd(k + 1, b − 1) = 1. numbers that are a power of 2. If the only Fermat numbers are the five known, then 216 2n + 1 would be composite for n > 0, and therefore 216 = 65536 would be the least Sierpiński number, not Selfridge’s ...
... ‡ Just those smaller than conjectured least base b Sierpiński and with gcd(k + 1, b − 1) = 1. numbers that are a power of 2. If the only Fermat numbers are the five known, then 216 2n + 1 would be composite for n > 0, and therefore 216 = 65536 would be the least Sierpiński number, not Selfridge’s ...
Collatz conjecture
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem; the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud), or as wondrous numbers.Take any natural number n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 1 to obtain 3n + 1. Repeat the process (which has been called ""Half Or Triple Plus One"", or HOTPO) indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. The property has also been called oneness.Paul Erdős said about the Collatz conjecture: ""Mathematics may not be ready for such problems."" He also offered $500 for its solution.