Răspuns: [tex]\bf n = (5^{4}\cdot 2)^{2} \implies patrat\:perfect[/tex]
Explicație pas cu pas:
Salutare !
[tex]\bf n = [(5^{3})^{7} :(1+2^{2})^{10} -5^{10}] :5^{2}[/tex]
[tex]\bf n = [5^{3\cdot 7} :(1+4 )^{10} -5^{10}] :5^{2}[/tex]
[tex]\bf n = [5^{21} :5^{10} -5^{10}] :5^{2}[/tex]
[tex]\bf n = (5^{21-10} -5^{10}) :5^{2}[/tex]
[tex]\bf n = (5^{11} -5^{10}) :5^{2}[/tex]
[tex]\bf n = 5^{10}\cdot (5^{11-10} -5^{10-10}) :5^{2}[/tex]
[tex]\bf n = 5^{10}\cdot (5^{1} -5^{0}) :5^{2}[/tex]
[tex]\bf n = 5^{10}\cdot (5-1) :5^{2}[/tex]
[tex]\bf n = 5^{10-2}\cdot 4[/tex]
[tex]\bf n = 5^{8}\cdot 2^{2}[/tex]
[tex]\bf n = (5^{4}\cdot 2)^{2} \implies patrat\:perfect[/tex]
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