CHECKING THE ODD GOLDBACH CONJECTURE UP TO 10 1
... such that every integer is the sum of at most S primes [6], and (ii) every sufficiently large even integer may be written as the sum of a prime number and of the product of at most two prime numbers [3]. On the other hand, this conjecture has been numerically verified up to 4 × 1011 [7]. This conjec ...
... such that every integer is the sum of at most S primes [6], and (ii) every sufficiently large even integer may be written as the sum of a prime number and of the product of at most two prime numbers [3]. On the other hand, this conjecture has been numerically verified up to 4 × 1011 [7]. This conjec ...
Full text
... r e p r e s e n t s the sum of the distinct divisors of n (not necessarily proper). Finally a number, n, is called weird* if it is abundant and not semiperfect. Are any Fibonacci or Lucas numbers weird? ...
... r e p r e s e n t s the sum of the distinct divisors of n (not necessarily proper). Finally a number, n, is called weird* if it is abundant and not semiperfect. Are any Fibonacci or Lucas numbers weird? ...
Warm Up
... Exit Ticket • 1. Create a real-life example that can be modeled by the expression −2 × 4, and then state the product. • 2. Two integers are multiplied, and their product is a positive number. What must be true about the two integers? ...
... Exit Ticket • 1. Create a real-life example that can be modeled by the expression −2 × 4, and then state the product. • 2. Two integers are multiplied, and their product is a positive number. What must be true about the two integers? ...
ESSNER EXAM 2002-2003
... 7. Given a triangle whose sides are of length 3,4,5, if h is the length of the altitude to the longest side then h equals (a) 5/2 (b) 8/3 (c) 9/4 (d) 7/3 (e) 12/5 8. For how many positive integers n are n, n + 2 and n + 4 all prime numbers? (a) none (b) 1 (c) 2 (d) more than 2 but a finite number (e ...
... 7. Given a triangle whose sides are of length 3,4,5, if h is the length of the altitude to the longest side then h equals (a) 5/2 (b) 8/3 (c) 9/4 (d) 7/3 (e) 12/5 8. For how many positive integers n are n, n + 2 and n + 4 all prime numbers? (a) none (b) 1 (c) 2 (d) more than 2 but a finite number (e ...
GRE MATH REVIEW #1 Basic Arithmetic whole numbers
... Basic Arithmetic The whole numbers, or counting numbers, are 0,1,2,3,4,5,6… The integers are …-4, -3, -2, -1,0,1,2,3,4… Recall the number line in deciding whether one negative number is larger than another. Positive integers increase as they move away from 0; negative integers decrease as they move ...
... Basic Arithmetic The whole numbers, or counting numbers, are 0,1,2,3,4,5,6… The integers are …-4, -3, -2, -1,0,1,2,3,4… Recall the number line in deciding whether one negative number is larger than another. Positive integers increase as they move away from 0; negative integers decrease as they move ...
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.