Wat is de grootste priemfactor van (25!) ^ 3 - (24!) ^ 3?

Wat is de grootste priemfactor van (25!) ^ 3 - (24!) ^ 3?
Anonim

Antwoord:

#31#

Uitleg:

#(25!)^3-(24!)^3 = (25*24!)^3-(24!)^3 = 25^3(24!)^3-(24!)^3#

#=(25^3-1)(24!)^3 = (15625-1)(24!)^3 = 15624(24!)^3#

#15624 = 2^3*3^2*7*31#

De grootste priemfactor van #(24!)^3# is de grootste priemfactor van #24!# welke is #23#