First slide

Introduction to P.M.I

Question

If $x^{2 n - 1} + y^{2 n - 1}$ is divisible by x+y ,if n is

Moderate

A

a positive integer
B

an even positive integer
C

an odd positive integer
D

None of the above

Solution

Let
$\begin{matrix} P (n) \equiv x^{2 n - 1} + y^{2 n - 1} = λ (x + y) \\ P (1) \equiv x + y = λ_{1} (x + y) \\ P (2) \equiv x^{3} + y^{3} = λ_{2} (x + y) \end{matrix}$

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