Related Experiment Video
Updated: Dec 4, 2025
07:44
Design and Synthesis of a Reconfigurable DNA Accordion Rack
Published on: August 15, 2018
7.3K
Tribonacci numbers that are concatenations of two repdigits
1Institute of Analysis and Number Theory, University of Technology, Kopernikusgasse 24/II, 8010 Graz, Austria.
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales. Serie A, Matematicas
|October 22, 2020
Summary
This study identifies all Tribonacci numbers that are formed by concatenating two identical digits. Researchers utilized advanced number theory techniques to solve this specific problem in the Tribonacci sequence.
Area of Science:
- Number Theory
- Algebraic Number Theory
Background:
- The Tribonacci sequence is defined by a linear recurrence relation.
- Repdigits are numbers consisting of repeating digits.
- Investigating number properties within sequences is a common area of mathematical research.
Purpose of the Study:
- To find all Tribonacci numbers that are concatenations of two repdigits.
- To apply advanced techniques from Diophantine equations and algebraic number theory.
Main Methods:
- Utilizing lower bounds for linear forms in logarithms of algebraic numbers.
- Employing the Baker-Davenport reduction procedure.
- Combining these methods to constrain the possible solutions.
Main Results:
- All Tribonacci numbers that are concatenations of two repdigits have been identified.
- The specific Tribonacci numbers satisfying this property were determined through the application of the described methods.
Conclusions:
- The study successfully characterized a specific subset of Tribonacci numbers.
- The findings demonstrate the effectiveness of using logarithmic forms and reduction techniques in number theory problems.
Related Concept Videos
01:30Binomial Expansion Using Pascal's Triangle
84
Expanding a binomial expression such as (a + b)n results in a predictable sequence of terms that can be systematically derived using Pascal’s Triangle. This triangular array of numbers plays a central role in understanding and computing the coefficients of binomial expansions.Pascal’s Triangle is constructed such that each row corresponds to the coefficients of a binomial raised to a power. The topmost row, known as the zeroth row, corresponds to (a + b)0, and each successive row...
84
01:30The Binomial Theorem
89
The Binomial Theorem is a foundational principle in algebra used to expand expressions raised to a power. It provides a structured approach for expanding binomials of the form (a+b)n, where a and b are variables or constants representing algebraic expressions, and n is a non-negative integer.The general form of the Binomial Theorem is:Each term in the expansion involves a binomial coefficient, which is calculated using factorials:The exponent of a in each term decreases from n to 0, while the...
89
01:30Geometric Sequences
130
In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...
130
01:29Sequences
119
Sequences are fundamental mathematical objects consisting of ordered lists of numbers that follow a specific rule or pattern. Sequences are critical in various mathematical concepts, including calculus, series, and number theory. They can model real-world phenomena such as population growth, financial investments, and physical processes like the diminishing height of a bouncing ball.Each number in a sequence is referred to as a term. Typically, the terms are denoted as a1, a2, a3,…, where...
119
01:17Trigonometric Fourier series
618
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
618
01:27Trigonometric Identities III
72
Cofunction identities are a key concept in trigonometry. They describe how trigonometric functions relate when their input angles are complementary — meaning the angles add up to 90°. On the unit circle, every angle θ— measured counterclockwise from the positive x-axis — corresponds to a point with coordinates (cos θ, sin θ). These values represent the horizontal and vertical components of the terminal side of the angle.If the same point on...
72