Stop Growing!
... You are given five integers: A0, B0, C0, D0 and E0. Each number in the sequence, Ak, Bk, Ck, Dk and Ek are calculated by the following formula: Ak ...
... You are given five integers: A0, B0, C0, D0 and E0. Each number in the sequence, Ak, Bk, Ck, Dk and Ek are calculated by the following formula: Ak ...
24. Prove that every integer greater than 11 can be expressed as th
... integer. Reference to algebra texts or experimentation shows that 2ab − 1 factors as (2a − 1)(2(b−1)a + 2(b−2)a + · · · + 22a + 2a + 1) and by closure both are integers. Now since a > 1, the factor 2a − 1 does not equal 1, and since b > 1, the other factor has at least two terms; that is, it is equa ...
... integer. Reference to algebra texts or experimentation shows that 2ab − 1 factors as (2a − 1)(2(b−1)a + 2(b−2)a + · · · + 22a + 2a + 1) and by closure both are integers. Now since a > 1, the factor 2a − 1 does not equal 1, and since b > 1, the other factor has at least two terms; that is, it is equa ...
2 + 4 + 6 = 12
... • Be sure to come and talk to me if you missed more than you got right and you do not understand why the answers you had were wrong. • Record the number you get right on your portfolio sheet! ...
... • Be sure to come and talk to me if you missed more than you got right and you do not understand why the answers you had were wrong. • Record the number you get right on your portfolio sheet! ...
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.