Gazeta Matematică nr 4 2018

S:E18.154 (Nicolae Mușuroia) - soluție

Fie $a,b,c\in \mathbb {Z}$ cu 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 b^{2}+c^{2}=a^{2}} . Arătați că pentru orice 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\in \mathbb{N}^{*}} , ecuația 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 x^{2}+2a^{n}x+b^{2n}+c^{2n}=0} are soluții reale.