Gazeta Matematică nr 4 2018

S:E18.154 (Nicolae Mușuroia) - soluție

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