Question

Let x, y be real numbers such that the numbers x + y and xy are integers.
Prove that for all positive integers n, the number x^n + y^n is an integer.

Answer 1

Answer:

use pmi

Step-by-step explanation:

so here lets take (x^n + y^n)

now fr n=1 its x+y and its an integer

so let it be true for x^k + y^k

now prove the product of x^k+1 and y^k+1 to be an integer as well so

(x^k+y^k)xy= x^k+1y + y^k+1x so here its an integer too as xy is also an integer....... thus x^n+y^n is also an integer for every x,y belongs to R and n belongs to R