Catalan pseudoprimes - Research in Scientific Computing in
... Values of ac(n): much information from computation, many questions, few answers (yet) • The curves around 1/3 seem to be described by ac(3p)= 1/3 1/p where p ranges over certain, but not all, primes? Is this true? Which primes? • Specific reduced fractional values of ac(n) seem to occur relativel ...
... Values of ac(n): much information from computation, many questions, few answers (yet) • The curves around 1/3 seem to be described by ac(3p)= 1/3 1/p where p ranges over certain, but not all, primes? Is this true? Which primes? • Specific reduced fractional values of ac(n) seem to occur relativel ...
Problem Sessions 1 - University of Nebraska–Lincoln
... a. Write the corresponding divisibility statement for each expression. (For example, a0 corresponds to the divisibility statement a|0.) Using the definition of divides, determine which of these divisibility statements are true. b. Only one expression determines a unique numerical value. Using your r ...
... a. Write the corresponding divisibility statement for each expression. (For example, a0 corresponds to the divisibility statement a|0.) Using the definition of divides, determine which of these divisibility statements are true. b. Only one expression determines a unique numerical value. Using your r ...
Improper fractions and mixed numbers
... An improper fraction is a positive fraction that is expressed with a numerator and a denominator, the numerator being greater than the denominator. A mixed number is a number expressed as the sum of a whole number and a proper fraction, which is a positive fraction that is expressed with a numerator ...
... An improper fraction is a positive fraction that is expressed with a numerator and a denominator, the numerator being greater than the denominator. A mixed number is a number expressed as the sum of a whole number and a proper fraction, which is a positive fraction that is expressed with a numerator ...
Practice Problems 1 - Fitchburg State University
... Each of the difference items in the table is the difference between the number to its left (or West) the number to its left and down (or Southwest) except that for numbers in the bottom right corner, since I couldn't subtract I just left them blank. But looking at the columns, it's easy to believe t ...
... Each of the difference items in the table is the difference between the number to its left (or West) the number to its left and down (or Southwest) except that for numbers in the bottom right corner, since I couldn't subtract I just left them blank. But looking at the columns, it's easy to believe t ...
Farey Sequences and Applications
... Euler’s Totient Function To construct an equation for the number of elements in a Farey Sequence, we must first understand the concept of Euler’s Totient Function. Euler’s Totient function represents the number of positive integers less than a number n that are coprime to n. It is represented as th ...
... Euler’s Totient Function To construct an equation for the number of elements in a Farey Sequence, we must first understand the concept of Euler’s Totient Function. Euler’s Totient function represents the number of positive integers less than a number n that are coprime to n. It is represented as th ...
Letter to the Editor
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
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.