AP EAMCET · Maths · Basic of Mathematics
For what values of \(m \in N\), the following divisibility \(x+y / x^m+y^m\) holds?
- A even numbers
- B odd numbers
- C all-natural numbers
- D only when \(m=1\)
Answer & Solution
Correct Answer
(B) odd numbers
Step-by-step Solution
Detailed explanation
Value of \(m \in N\) for which \(x^m+y^m\) is divisible by \(x+y\). Let \(P(m)=x^m+y^m\) is divisible by \(x+y\). Let us consider \(m=1\). \(P(1): x+y\) is divisible by \(x+y ; \therefore P(1)\) is true \(\Rightarrow m=2 \Rightarrow P(2): x^2+y^2\) is divisible by \(x+y\) which…
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