**Volume 17** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Two modifications of Klamkin’s inequality**

*Original research paper. Pages 1—3*

Krassimir T. Atanassov

Full paper (PDF, 82 Kb) | Abstract

**A novel approach to the discovery of ternary BBP—type formulas for polylogarithm constants**

*Original research paper. Pages 4—20*

Kunle Adegoke

Full paper (PDF, 207 Kb) | Abstract

**On construction of rhomtrees as graphical representation of rhotrices**

*Original research paper. Pages 21—29*

A. Mohammed and B. Sani

Full paper (PDF, 153 Kb) | Abstract

**A note of diagonalization of integral quadratic forms modulo p^{m}**

*Original research paper. Pages 30—36*

Ali H. Hakami

Full paper (PDF, 171 Kb) | Abstract

*m*be a positive integer,

*p*be an odd prime, and ℤ

*= ℤ / (*

_{pm}*p*) be the ring of integers modulo

^{m}*p*. Let

^{m}*Q*(

**x**) =

*Q*(

*x*

_{1},

*x*

_{2}, …,

*x*) be a nonsingular quadratic form with integer coefficients. In this paper we shall prove that any nonsingular quadratic form

_{n}*Q*(

**x**) over ℤ,

*Q*(

**x**) is equivalent to a diagonal quadratic form (modulo

*p*).

^{m}**Why are some right-end digits absent in primitive Pythagorean triples?**

*Original research paper. Pages 37—44*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 171 Kb) | Abstract

_{3}shows that the right-end digit (RED) couples (1,4), (5,6) and (5,0) for

*x*

^{2},

*y*

^{2}in the primitive Pythagorean triple (pPt) in the equation

*z*

^{2}=

*x*

^{2}+

*y*

^{2}do not lead to the primitive form of triple. The rows of

*x*

^{2},

*y*

^{2}with these REDs do not add to the required form for

*z*

^{2}. Since 3 ∤

*z*, the row of

*z*

^{2}must follow the pentagonal numbers. Common factors for

*x*,

*y*are also inconsistent with pPt formation so that the (

*x*

^{2},

*y*

^{2}). RED (5,0) may be discarded directly.

**Volume 17**▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4