E:15991

E-15991 (Cristina Vijdeluc și Mihai Vijdeluc, Baia Mare )

Aflați numerele naturale Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} și Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abc}} pentru care Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abc}\cdot p^4=\overline{3abc}} .

Soluție:

Din Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \overline{abc}\cdot n^4=\overline{3abc}} rezultă ${\overline {abc}}\cdot n^{4}=300+{\overline {abc}}$ și apoi ${\overline {abc}}\cdot (n^{4}-1)=300$.

Pentru $n=2$ se obține ${\overline {abc}}=200$.

Pentru restul valoriilor naturale ale lui Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} nu se obțin soluții convenabile.