National and Regional Contests Turkey Contests National Olympiad First Round 2002 National Olympiad First Round 2 P02 [Number Theory] - Turkish NMO 1st Round - 2002 Problem Statement What is 3 2002 3^{2002} 3 2002 m o d 11 \bmod 11 mod 11 < s p a n c l a s s = ′ l a t e x − b o l d ′ > a ) < / s p a n > 1 < s p a n c l a s s = ′ l a t e x − b o l d ′ > b ) < / s p a n > 3 < s p a n c l a s s = ′ l a t e x − b o l d ′ > c ) < / s p a n > 4 < s p a n c l a s s = ′ l a t e x − b o l d ′ > d ) < / s p a n > 5 < s p a n c l a s s = ′ l a t e x − b o l d ′ > e ) < / s p a n > None of above
<span class='latex-bold'>a)</span>\ 1
\qquad<span class='latex-bold'>b)</span>\ 3
\qquad<span class='latex-bold'>c)</span>\ 4
\qquad<span class='latex-bold'>d)</span>\ 5
\qquad<span class='latex-bold'>e)</span>\ \text{None of above}
< s p an c l a ss = ′ l a t e x − b o l d ′ > a ) < / s p an > 1 < s p an c l a ss = ′ l a t e x − b o l d ′ > b ) < / s p an > 3 < s p an c l a ss = ′ l a t e x − b o l d ′ > c ) < / s p an > 4 < s p an c l a ss = ′ l a t e x − b o l d ′ > d ) < / s p an > 5 < s p an c l a ss = ′ l a t e x − b o l d ′ > e ) < / s p an > None of above