Question Number 77915 by naka3546 last updated on 12/Jan/20
$${Find}\:\:{prime}\:\:{factor}\:\:{of}\:\:\mathrm{4}^{\mathrm{8}} \:−\:\mathrm{3}^{\mathrm{8}} \:\: \\ $$
Answered by jagoll last updated on 12/Jan/20
$$\mathrm{4}^{\mathrm{8}} −\mathrm{3}^{\mathrm{8}} =\:\left(\mathrm{4}^{\mathrm{4}} −\mathrm{3}^{\mathrm{4}} \right)\left(\mathrm{4}^{\mathrm{4}} +\mathrm{3}^{\mathrm{4}} \right) \\ $$$$=\:\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{337}\right) \\ $$$$=\:\left(\mathrm{4}−\mathrm{3}\right)\left(\mathrm{4}+\mathrm{3}\right)\left(\mathrm{25}\right)\left(\mathrm{337}\right) \\ $$$$=\mathrm{1}×\mathrm{7}×\mathrm{5}^{\mathrm{2}} ×\mathrm{337} \\ $$$${prime}\:{factor}\::\:\mathrm{5},\:\mathrm{7},\:\mathrm{337} \\ $$