IN the published correspondence of Euler there is a note from him to Goldbach, or, the other way, from Goldbach to Euler, in which a very wonderful theorem is stated which has never been proved by ...

Abstract: This paper is about Jacobi’s triple product identity and Euler’s pentagonal number theorem. To be specific, it gives the proofs of Jacobi’s triple product identity via Gaussian polynomials ...

https://doi.org/10.4169/amer.math.monthly.118.03.217 https://www.jstor.org/stable/10.4169/amer.math.monthly.118.03.217 Abstract We strengthen a result of Lehmer ...

Abstract: In edge-fog computing networks, it is very crucial to ensure that group keys are secure and reliable. In recent years, there has been much interest in group key updating schemes based on ...

Sometimes the greatest revolutions in Mathematics are not theorems or proofs, but changes of notation. The greatest revolution in notation may have been the introduction of the place-value system to ...