Răspuns: 4 pătrate perfecte divid numarul n
Explicație pas cu pas:
Salutare!
[tex]\bf 2^{2} \longrightarrow patrat~perfect[/tex]
[tex]\bf 3^{2} \longrightarrow patrat~perfect[/tex]
[tex]\bf 3^{4} \longrightarrow patrat~perfect[/tex]
[tex]\bf 5^{2} \longrightarrow patrat~perfect[/tex]
[tex]\bf ~~~~[/tex]
[tex]\bf n = 2^{10} \cdot 3^{4}\cdot 5^{2}[/tex]
[tex]\bf n = (2^{5})^{2}\cdot (3^{2})^{2}\cdot 5^{2}[/tex]
[tex]\bf n = 2^{5}\cdot 2^{2}\cdot 3^{2}\cdot 3^{2}\cdot 5^{2}\implies n~\vdots~2^{2},~3^{2},3^{4},~5^{2}[/tex]
[tex]\bf~~~[/tex]
[tex]\bf 4~patrate ~perfecte~divid~numarul~n[/tex]
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