On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties.
On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
On some arithmetical properties of Lucas and Lehmer numbers
On some arithmetical properties of weighted sums of S-units.
On some Diophantine equations. I.
On some Diophantine equations. II.
On some Diophantine equations. III.
On Some Elliptic Curves Defined Over ... of Free Rank ... 9.
On some elliptic curves with large sha.
On some equations over finite fields
In this paper, following L. Carlitz we consider some special equations of variables over the finite field of elements. We obtain explicit formulas for the number of solutions of these equations, under a certain restriction on and .
On some expressions associated with Fermat's last theorem.
On some generalizations of the diophantine equation
On some generalizations of the diophantine equation
On some inequalities connected with Fermat's equation.
On some properties of two simultaneous polygonal sequences.
On some special forms of simultaneous Pell equations
On Some Ternary Quartic Diophantine Equations.
On some universal sums of generalized polygonal numbers
For m = 3,4,... those pₘ(x) = (m-2)x(x-1)/2 + x with x ∈ ℤ are called generalized m-gonal numbers. Sun (2015) studied for what values of positive integers a,b,c the sum ap₅ + bp₅ + cp₅ is universal over ℤ (i.e., any n ∈ ℕ = 0,1,2,... has the form ap₅(x) + bp₅(y) + cp₅(z) with x,y,z ∈ ℤ). We prove that p₅ + bp₅ + 3p₅ (b = 1,2,3,4,9) and p₅ + 2p₅ + 6p₅ are universal over ℤ, as conjectured by Sun. Sun also conjectured that any n ∈ ℕ can be written as and 3p₃(x) + p₅(y) + p₇(z) with x,y,z ∈ ℕ; in...
On Sophie Germain type criteria for Fermat's Last Theorem
On square values of quadratics