S:E15.208

S:E15.208 (Angela Lopată)

Determinați toate numerele naturale consecutive care au suma $2015$.

Soluția 1 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\in \mathbb{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 N\in \mathbb{N}\setminus\left\{0,1\right\}} numere naturale pentru care

$$\left(a+1\right)+\left(a+2\right)+\ldots +\left(a+N\right)=2015.$$

În mod echivalent, se obține

$$Na+\left(1+2+\ldots +N\right)=2015,$$

deci

$$N\cdot \left(2a+1+N\right)=2\cdot 2015.$$