Răspuns :
Răspuns:
[tex] \color{cc0000} \boxed{\huge \bf m - n = 1345}[/tex]
Explicație pas cu pas:
Salutare!
[tex] \bf {10}^{n - 1} \leqslant a < {10}^{n} \implies {10}^{2n - 5} \leqslant {a}^{5} < {10}^{5n}[/tex]
[tex] \bf Dar \: {10}^{m- 1} \leqslant {a}^{5} < {10}^{m} \: \: avem :[/tex]
[tex] \bf {10}^{m - 1} \leqslant {a}^{5} < {10}^{n} \implies m - 1 < 5n[/tex]
[tex] \bf {10}^{5n - 5} \leqslant {a}^{5} < {10}^{m} \implies 5n - 5< 5m[/tex]
[tex] \bf Din \: cele \: de \: mai \: sus \: vom \: avea:5n - 5 < m < 5n + 1 \implies[/tex]
[tex] \bf 5n - 5 < 2019 - n < 5n + 1 \implies2018 < 6n < 2024 \: \bigg|:6[/tex]
[tex] \bf \implies \boxed{ \large \bf n = 337} \: \: si \: \: \boxed{ \large \bf m = 1682}[/tex]
[tex] \color{cc0000} \boxed{ \large \bf m - n = 1682 - 337 = \boxed{\large \bf 1345}}[/tex]
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