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Sa se determine n stiind ca 5 la puterea n+5 la puterea n+1+5 la puterea n+2=675

Răspuns :

[tex]5^n+5^{n+1}+5^{n+2}=675\\ 5^n(1+5+5^2)=675\\ 5^n\cdot 31=675\\ 5^n= \frac{675}{31} \notin N\\ Nu\ exista\ n\ numar\ natural\ care\ sa\ verifice\ ecuatia.[/tex]