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Problem #25 · August 21, 2026

Divisibility rules

The sum of three consecutive natural numbers always:
  1. Ais divisible by 2
  2. Bis divisible by 3
  3. Cis divisible by 6
  4. Dis divisible by 9
  5. Eis an odd number

WORKED EXAMPLE

Solution

Denote the three consecutive numbers by n−1n-1, nn, and n+1n+1. Their sum is (n−1)+n+(n+1)=3n(n-1)+n+(n+1) = 3n, which is always divisible by 33. The other statements do not always hold: for example, 2+3+4=92+3+4=9 is odd and not divisible by 66, while 1+2+3=61+2+3=6 is even and not divisible by 99.
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