![King's Maths School [logo]](/image-library/logos/kcl-ms-logo.jpg){kind=logo}
Challenge 283: Simplifying Surds
Does this surd expression always simplify to an integer?
Prove that
(2 + √2)(3 - 2√2)n + (2 - √2)(3 + 2√2)n
is an integer for every positive integer n.
Does this surd expression always simplify to an integer?
Prove that
(2 + √2)(3 - 2√2)n + (2 - √2)(3 + 2√2)n
is an integer for every positive integer n.