Question

sa se arate ca numarul 7×32^37-7^14 este divizibil cu 5​

Answer 1

$U(7\cdot 32^{37}-7^{14}) =\\ \\ =U(7\cdot 2^{37}-7^{14})= \\ \\= U(7\cdot 2^{4\cdot 9}\cdot 2 - 7^{4\cdot 3}\cdot 7^2) \\ \\ = U\Big(7\cdot 16^9\cdot 2 - (7^4)^3\cdot 7^2\Big) = \\ \\ = U(7\cdot 6\cdot 2-1^3\cdot 7^2) = \\ \\ =U(42\cdot 2 - 7^2) = \\ \\= U(84 - 49) = \\ \\ =U(35) \\ \\ =5\\ \\\\ \Rightarrow 7\cdot 32^{37}-7^{14}\,\,\vdots\,\, 5$