a=(25^n :5⁵ +3⁴ -4³ +5^n) *[(2⁵ -5² -7 ) :2001]+2002=
=(25^n :5⁵ +3⁴ -4³ +5^n) *[(32-25 -7 ) :2001]+2002=
=(25^n :5⁵ +3⁴ -4³ +5^n) *[ 0 :2001]+2002=
=(25^n :5⁵ +3⁴ -4³ +5^n) * 0 +2002= 2002
b=(32 * 1999⁵ +3998 ⁵ + 2³*3*8³) * (111 ³ *125 -555³) =
=(32 * 1999⁵ +3998 ⁵ + 2³*3*8³) *(111³ *5³ -111³*5³) =
=(32 * 1999⁵ +3998 ⁵ + 2³*3*8³) *0=0
c=10³ + 9*10² +9*10+11
=
=10²(10 + 9) +90+11
=
=10² *19 +90+11
=
=1900+101=2001
(a-b-c)²⁰⁰¹=(2002-0-2001)²⁰⁰¹=1²⁰⁰¹=1