The difference between the squares of two consecutive odd integers is always divisible by · ABC26GN0303
Subject: General Aptitude · Chapter: Number System
The difference between the squares of two consecutive odd integers is always divisible by
Answer
Explanation
Let the two consecutive odd integers be (2m + 1) and (2m + 3). Then, (2m + 3)2 – (2m + 1)2 = [(2m + 3) + (2m + 1)] [(2m + 3) – (2m + 1)] = (4m + 4) × 2 = 8m + 8 = 8(m + 1), which is always divisible by 8. NUMBER SYSTEM
Explanation as extracted from the printed page; notation may be imperfect.
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