[tex]\bf 4\cdot 3^{5n+2}-7\cdot3^{5n+1}+5\cdot3^{5n} =[/tex]
[tex]\bf 3^{5n}\cdot(4\cdot 3^{5n+2-5n}-7\cdot3^{5n+1-5n}+5\cdot3^{5n-5n})=[/tex]
[tex]\bf 3^{5n}\cdot(4\cdot 3^{2}-7\cdot3^{1}+5\cdot3^{0})=[/tex]
[tex]\bf 3^{5n}\cdot(4\cdot 9-7\cdot3+5\cdot1)=[/tex]
[tex]\bf 3^{5n}\cdot(36-21+5)=[/tex]
[tex]\bf 3^{5n}\cdot 20 =[/tex]
[tex]\bf 3^{5n}\cdot 2\cdot 10[/tex] este divizibil cu 10,∀ n ∈ IN
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Raspuns: [tex]\bf 4\cdot 3^{5n+2}-7\cdot3^{5n+1}+5\cdot3^{5n}[/tex] ⋮ 10, ∀ n ∈ IN*
