This paper presents a brief demonstration of Scholz’s third conjecture [1] for n numbers such that their minimum chain addition is star type [2]. The demonstration is based on the proposal of an algorithm that takes ...This paper presents a brief demonstration of Scholz’s third conjecture [1] for n numbers such that their minimum chain addition is star type [2]. The demonstration is based on the proposal of an algorithm that takes as input the star-adding chain of a number n, and returns a string in addition to x = 2n - 1??of length equal to l (n) + n - 1. As for any type addition chain star of a number n, this chain is minimal demonstrates the Scholz’s third Conjecture for such numbers.展开更多
This paper presents a brief demonstration of Schulz’s first conjecture, which sets the upper and lower limits on the length of the shortest chain of addition. Two methods of the upper limit are demonstrated;the secon...This paper presents a brief demonstration of Schulz’s first conjecture, which sets the upper and lower limits on the length of the shortest chain of addition. Two methods of the upper limit are demonstrated;the second one is based on the algorithm of one of the most popular methods for obtaining addition chains of a number, known as the binary method.展开更多
文摘This paper presents a brief demonstration of Scholz’s third conjecture [1] for n numbers such that their minimum chain addition is star type [2]. The demonstration is based on the proposal of an algorithm that takes as input the star-adding chain of a number n, and returns a string in addition to x = 2n - 1??of length equal to l (n) + n - 1. As for any type addition chain star of a number n, this chain is minimal demonstrates the Scholz’s third Conjecture for such numbers.
文摘This paper presents a brief demonstration of Schulz’s first conjecture, which sets the upper and lower limits on the length of the shortest chain of addition. Two methods of the upper limit are demonstrated;the second one is based on the algorithm of one of the most popular methods for obtaining addition chains of a number, known as the binary method.
