Another easy problem.
Number Theory
Level
2
Find the remainder when is divided by .
The answer is 7.
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1 solution
All congruences are ( m o d 9 ) .
4 4 4 4 ≡ 7 therefore 4 4 4 4 3 ≡ 7 3 ≡ 1 hence 4 4 4 4 4 4 4 4 = ( 4 4 4 4 3 ) 1 4 8 1 × 4 4 4 4 ≡ 1 × 7 = 7