Answer:
Step-by-step explanation:
Given (12^13–12^12+12^11)(11^9–11^8+11^7),
(12^13–12^12+12^11)(11^9–11^8+11^7) =
[(12^12)12 – 12^12 + 12^11][(11^8)11 – 11^8 + 11^7)
[(12^12)(12 – 1) + 12^11][(11^8)(11 – 1) + 11^7] =
(12^12(11) + 12^11)(11^8(10) + 11^7) =
(12^11(12x11) + 12^11)(11^7(11x10) + 11^7) =
[(12^11)(12x11 + 1)][(11^7)(11x10 + 1)] =
[(12^11)x(11^7)](12x11 + 1)(11x10 + 1) =
[(12^11)x(11^7)](133 x 111) =
[(12^11)x(11^7)](133 x 111) =
[(12^11)x(11^7)](14763) =
[(12^11)x(11^7)](3x7x19x37)
From here, it is clear that the given number is divisible by 3, 7, 19 and 37.
