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Prove that one of any three consecutive positive integers must be divisible by 3. |
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Answer» Let 3 consecutive positive integers be n, n+1 and n+2 Whenever a number is divided by 3, the remainder we get is either 0, or 1, or 2. : Therefore: n = 3p or 3p+1 or 3p+2, where p is some integer If n = 3p, then n is divisible by 3 If n = 3p +1, then n+2 = 3p+1+2 = 3p+3 = 3(p+1) is divisible by 3 If n = 3p +2, then n+1 = 3p+2+1 = 3p+3 = 3(p+1) is divisible by 3 Thus, we can state that one of the numbers among n, n+1 and n+2 is always divisible by 3. |
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