Question

Arătati că: a) 5^47|25^25; b) 49^19|7^20 ; Am nevoie de ajutor !
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Answer 1

$\displaystyle\bf\\primul~sub~punct~este~gresit,~corectare~:~25^{25} \vdots 5^{47}.\\a)~25^{25} \vdots 5^{47} \Leftrightarrow (5^2)^{25} \vdots5^{47} \Leftrightarrow 5^{50} \vdots 5^{47} \Leftrightarrow \frac{5^{50}}{5^{47}} \in \mathbb N \Leftrightarrow 5^3 \in \mathbb N ,~ceea~ce~este~adevarat.\\b)~49^{19} \vdots7^{20} \Leftrightarrow (7^2)^{19} \vdots 7^{20} \Leftrightarrow 7^{38} \vdots 7^{20}\Leftrightarrow \frac{7^{38}}{7^{20}} \in \mathbb N \Leftrightarrow 7^{18} \in \mathbb N,~ceea~ce~este~adevarat.$