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Full-Text Articles in Physical Sciences and Mathematics
Solution Of The Diophantine Equation (Maa+Nbb)=Cd(Mcc+Ndd) Using Rational Numbers, Georg Ehlers
Solution Of The Diophantine Equation (Maa+Nbb)=Cd(Mcc+Ndd) Using Rational Numbers, Georg Ehlers
Euleriana
This paper (E716) was published in Nova acta Academiae scientiarum imperialis petropolitanae, Volume 13 (1795/96), pp. 45-63. It was also included in Commentationes Arithmeticae, Volume II, as Number LXVIII, pp. 281-293 (E791). Euler starts with Fermat's Last Theorem and mentions the proofs for the cases n=3 and n=4 which he had completed himself earlier. He then moves on to make the sum of powers conjecture, which was later disproved in the second half of the 20th century. In this context he discusses his discovery of 134^4+133^4=158^4+59^4, which he calls unexpected. Euler derives the title equation from A^4+B^4=C^4+D^4, generalizing it to …
Euler Archive Spotlight, Erik R. Tou
Euler Archive Spotlight, Erik R. Tou
Euleriana
A survey of two translations posted to the Euler Archive in 2022.
Euler's Anticipations, Christopher Goff, Erik Tou
Euler's Anticipations, Christopher Goff, Erik Tou
Euleriana
Welcome to Volume 3 of Euleriana. This issue highlights occasions where Euler's work anticipated future results from other others, sometimes by decades or even centuries!