The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a linear
recurrence sequence is the union of a finite set and finitely many arithmetic progressions …

It is a longstanding open problem whether there is an algorithm to decide the Skolem
Problem for linear recurrence sequences (LRS) over the integers, namely whether a given …

In this short note we give all solutions to the exponential Diophantine equation (4m^ 2+ 1)^
x+ (5m^ 2-1)^ y=(3m)^ z (4 m 2+ 1) x+(5 m 2-1) y=(3 m) z where 20< m< 90 20< m< 90 and …

Let m be a positive integer, and let p be a prime with p ≡ 1~(mod~ 4). p≡ 1 (mod 4). Then
we show that the exponential Diophantine equation (3pm^ 2-1)^ x+ (p (p-3) m^ 2+ 1) …

For any fixed relatively prime positive integers $ a $, $ b $ and $ c $ with $\min\{a, b, c\}> 1$,
we prove that the equation $ a^ x+ b^ y= c^ z $ has at most two solutions in positive integers …

Let r, l, m be positive integers such that 2∤ r, 3∣ l and r> l, and let e (r, l, m)= min {rlm 2-1, r
(rl) m 2+ 1}. In 2020, Kizildere, Le and Soydan proved if 3∤ rm and e (r, l, m)> 30, then the …

On the exponential Diophantine equation (3m2 + 1)x + (qm2 − 1)y = (rm)z Page 1 SUT Journal
of Mathematics Vol. 56, No. 2 (2020), 147–158 On the exponential Diophantine equation (3m2 …

We give finiteness results concerning terms of linear recurrence sequences having a
representation as a linear combination, with fixed coefficients, of powers of fixed primes. On …

On the Exponential Diophantine Equation (4m2 + 1)x + (45m2 − 1)y = (7m)z 1 Introduction.
Page 1 International Journal of Algebra, Vol. 15, 2021, no. 4, 233 - 241 HIKARI Ltd, www.m-hikari.com …

Recently, mixed polynomial–exponential equations similar to the one in the title have been
considered by many authors. In these results a certain non-coprimality condition plays an …