Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
Consider the following statements: (1) $a^{n}+b^{n}$ is divisible by $a+b$ if $n=2k+1$, where $k$ is a positive integer. (2) $a^{n}-b^{n}$ is divisible by $a-b$ if $n=2k$, where $k$ is a positive integer. Which of the statements given above is/are correct?
(a)1 only
(b)2 only
(c)Both 1 and 2
(d)Neither 1 nor 2
Answer
Answer (as printed): C
Explanation
Clearly, (1) when $n$ is odd, $(a^{n}+b^{n})$ is divisible by $(a+b)$. So, (1) is true. (2) $(a^{n}-b^{n})$ is divisible by $(a-b)$ for all values of $n$. So, (2) is true.
Explanation as extracted from the printed page; notation may be imperfect.