Question

Calculati (a-b-c) la puterea 2001:
a=(25 la puterea n :5 la 5 +3 la 4 -4 la 3 +5 la n) *[(2 la 5 -5 la 2 -7 ) :2001]+2002;
b=(32*1999 la 5 -3998 la 5 + 2 la3 *3*8 la 3) * (111 la 3 * 125 -555) la 3
c=10 la 3 + 9* 10 la 2 +9*10+11

Answer 1

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