Find the remainder when 44444444 is divided by 9 SolutionIt

Find the remainder when 4444^4444 is divided by 9.

Solution

It is known that

444 - 2 (mod 9)
Replacing 4444 by -2,
we get (-2)⁴⁴⁴⁴ = 2⁴⁴⁴⁴
         = 2¹ . 2⁴⁴⁴³
         = 2. (2³)¹⁴⁸¹
         = 2. 8¹⁴⁸¹
Now, 8 – 1 (mod 9)
Replacing 8 by -1,
we get 2. (-1)¹⁴⁸¹ = - 2    [Since -2 7(mod 9)]
Therefore remainder is 7 when 4444⁴⁴⁴⁴ is divided by 9.