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Problem #36 · September 1, 2026

Divisibility rules

How many natural numbers from 100100 to 500500, when divided by 66, leave a remainder of 44?
  1. A66
  2. B67
  3. C68
  4. D82
  5. E83

WORKED EXAMPLE

Solution

The numbers sought have the form 6k+46k+4. The smallest in the interval is 100=6⋅16+4100 = 6 \cdot 16 + 4, and the largest is 496=6⋅82+4496 = 6 \cdot 82 + 4. Therefore, their number is 82−16+1=6782 - 16 + 1 = 67.
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