ODDS AND ENDS OF ODDS AND EVENS: AN INQUIRY INTO
... Well I think of the prime, actually not prime, but , (pause) I don’t know, I’m probably stumped. Uh, (pause) I guess maybe just look at simpler cases, just look at 3 and 5 and 7 and. . . ...
... Well I think of the prime, actually not prime, but , (pause) I don’t know, I’m probably stumped. Uh, (pause) I guess maybe just look at simpler cases, just look at 3 and 5 and 7 and. . . ...
Full text
... pronic number by finding an integer w(n) such that 4Ln +1 is a quadratic nonresidue modulo w(n). It may be noted that if Ln is a pronic number, then Ln is two times a triangular number. Our interest in this problem was prompted by Ming Luo's very nice paper entitled "On Triangular Lucas Numbers," [2 ...
... pronic number by finding an integer w(n) such that 4Ln +1 is a quadratic nonresidue modulo w(n). It may be noted that if Ln is a pronic number, then Ln is two times a triangular number. Our interest in this problem was prompted by Ming Luo's very nice paper entitled "On Triangular Lucas Numbers," [2 ...
11Numbers
... – Zero for positive number – One for negative number Examples – E.g., 0010 1100 44 – E.g., 1010 1100 -44 Hard to do arithmetic this way, so it is rarely used ...
... – Zero for positive number – One for negative number Examples – E.g., 0010 1100 44 – E.g., 1010 1100 -44 Hard to do arithmetic this way, so it is rarely used ...
The Pigeonhole Principle Recall that a function f
... day, and a total of 70 times in all. Show that there is a period of consecutive days during which he trains exactly 17 times. It will take some work before the pigeons can be described. Let x0 = 0 and, for i = 1, 2, . . . , 44, let xi be the number of times Gary trains up to the end of day i. Then 0 ...
... day, and a total of 70 times in all. Show that there is a period of consecutive days during which he trains exactly 17 times. It will take some work before the pigeons can be described. Let x0 = 0 and, for i = 1, 2, . . . , 44, let xi be the number of times Gary trains up to the end of day i. Then 0 ...
Powerpoint
... • Find the common ratio of the sequence 2, -4, 8, -16, 32, … • To find the common ratio, divide any term by the previous term. ...
... • Find the common ratio of the sequence 2, -4, 8, -16, 32, … • To find the common ratio, divide any term by the previous term. ...
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.