Djamel Himane

collaborators

3 papers

math.GM2024

A simple proof of Werner Schulte's conjecture

Djamel Himane

Lately, Werner Schulte has conjectured that for all positive $n > 1$ , $n$ divides $\frac{( n - 2 )! ( n - 1 )!}{2 ^{n - 3}} + 4$ if and only if $n$ is prime. In this paper, We use elementary me…

math.GM2024

Primitive Euler brick generator

Djamel Himane

The smallest Euler brick, discovered by Paul Halcke, has edges $(177, 44, 240)$ and face diagonals $(125, 267, 244)$ , generated by the primitive Pythagorean triple $(3, 4, 5)$ …

math.GM2024

A Pythagorean triangle in which the hypotenuse and the sum of the arms are squares

Djamel Himane

In this paper, show that the Diophantine equation $x^{2} + (x + 1)^{2} = w^{4}$ has only two solutions $(0, 1)$ and $(119, 13)$ in non-negative integers $x$ and $w$ . This equation conce…