In this paper, we show that there are no three distinct positive integers a, b, c such that ab+1, ac+1, bc+1 are all three Fibonacci numbers
Abstract Let n be any positive integer. We give a simple proof to the theorem that there always exis...
A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. Examples include...
In this two-part note, we study the following two problems. Given three positive integers a , b , c...
A Diophantine m-tuple is a set of {a1,..., am} of positive rational num-bers or integers such that a...
In this paper, we determine all the factorials that are a sum of at most three Fibonacci numbers
Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors
In this paper, we show that the diophantine equation Fn = pa ± pb has only finitely many positive in...
In this paper, we find all Fibonacci and Lucas numbers written in the form 2 a + 3 b + 5 c ...
In this paper, we define a Lucas-Lehmer type sequence denoted by (L-n)(n=0)(infinity), and show that...
Abstract. Fibonacci sequence stands as a kind of super sequence with fabulous properties. This note ...
In this paper, we find non-negative (n, m, a) integer solutions of the diophantine equation F-n-F-m ...
Let FL={1,2,3,4,5,7,8,11,13,18,21, … } be the set consisting of all Fibonacci and Lucas numbers with...
In the book Proofs that Really Count [1], the authors prove over 100 Fi-bonacci identities by combin...
Abstract: Let n be an integer. A set of positive integers is said to have the property D(n) if the p...
We show that there are only finitely many Diophantine quadruples, that is, sets of four positive int...
Abstract Let n be any positive integer. We give a simple proof to the theorem that there always exis...
A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. Examples include...
In this two-part note, we study the following two problems. Given three positive integers a , b , c...
A Diophantine m-tuple is a set of {a1,..., am} of positive rational num-bers or integers such that a...
In this paper, we determine all the factorials that are a sum of at most three Fibonacci numbers
Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors
In this paper, we show that the diophantine equation Fn = pa ± pb has only finitely many positive in...
In this paper, we find all Fibonacci and Lucas numbers written in the form 2 a + 3 b + 5 c ...
In this paper, we define a Lucas-Lehmer type sequence denoted by (L-n)(n=0)(infinity), and show that...
Abstract. Fibonacci sequence stands as a kind of super sequence with fabulous properties. This note ...
In this paper, we find non-negative (n, m, a) integer solutions of the diophantine equation F-n-F-m ...
Let FL={1,2,3,4,5,7,8,11,13,18,21, … } be the set consisting of all Fibonacci and Lucas numbers with...
In the book Proofs that Really Count [1], the authors prove over 100 Fi-bonacci identities by combin...
Abstract: Let n be an integer. A set of positive integers is said to have the property D(n) if the p...
We show that there are only finitely many Diophantine quadruples, that is, sets of four positive int...
Abstract Let n be any positive integer. We give a simple proof to the theorem that there always exis...
A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. Examples include...
In this two-part note, we study the following two problems. Given three positive integers a , b , c...
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