TY  - JOUR
T1  - Tribonacci numbers as sum or difference of powers of 2
AU  - Erduvan, Fatih
PY  - 2025
DA  - June
Y2  - 2025
DO  - 10.18466/cbayarfbe.1528991
JF  - Celal Bayar University Journal of Science
JO  - CBUJOS
PB  - Manisa Celal Bayar Üniversitesi
WT  - DergiPark
SN  - 1305-130X
SP  - 147
EP  - 151
VL  - 21
IS  - 2
LA  - en
AB  - This paper investigates Tribonacci numbers can be expressed as either the sum or difference of two distinct powers of 2. Namely, we address the problem of expressing Tribonacci numbers in the formT_n=2^x±2^y                                                                                                          in positive integers with 1≤y≤x. Our findings reveal specific instances where such representations are possible, including examples like the seventh Tribonacci number expressed both as the sum and the difference of powers of 2. Additionally, we identify Tribonacci numbers that can be represented as the differences of Mersenne numbers, specifically, the numbers 2, 4, 24, and 504. These results enhance the understanding of the structural properties of Tribonacci sequences and their relationships with exponential and Mersenne-based number systems.
KW  - Diophantine equations
KW  - Tribonacci numbers
KW  - Baker’s Theory
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UR  - https://doi.org/10.18466/cbayarfbe.1528991
L1  - https://dergipark.org.tr/tr/download/article-file/4125961
ER  -