Question

Precizeaza divizorii pentru urmatoarele numere naturale : A)2⁵⁰ B)3⁶¹ C)5⁵⁹ D)7⁴³​

Answer 1

   

$\displaystyle\bf\\Explicatii:\\\\\textbf{Divizorii unei puteri a unui numar prim sunt toate puterile}\\\textbf{acelui numar prim cu exponentii de la 0 pana la exponentul dat.}\\\\Se~da~p^k~unde:\\p=numar~prim\\k\in N\\\\D_{p^k}=\Big\{p^0;~p^1;~p^2;~p^3;~...;~p^k;~\Big\}\\\\Exemple:\\\\D_{2^2}=\{1;~2;~4\}=\Big\{2^0;~2^1;~2^2 \Big\}\\\\3^4=81\\D_{3^4}=\{1;~3;~9;~27;~81\}=\Big\{3^0;~3^1;~3^2;~3^3;~3^4 \Big\}$

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$\displaystyle\bf\\Rezolvare:\\\\A)~~2^{50}\\\\D_{\b2^{\b5\b0}}=\Big\{2^0;~2^1;~2^2;~2^3;~...;~2^{50} \Big\}\\\\\\B)~~3^{61}\\\\D_{\b3^{\b6\b1}}=\Big\{3^0;~3^1;~3^2;~3^3;~...;~3^{61} \Big\}\\\\\\C)~~5^{59}\\\\D_{\b5^{\b5\b9}}=\Big\{5^0;~5^1;~5^2;~5^3;~...;~5^{59}\Big\}\\\\\\D)~~7^{43}\\\\D_{\b7^{\b4\b3}}=\Big\{7^0;~7^1;~7^2;~7^3;~...;~7^{43}\Big\}$