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Prove that

(2 + √2)(3 - 2√2)ⁿ + (2 - √2)(3 + 2√2)ⁿ

is an integer for every positive integer n.

 +-----+------+-----+----+
 | NN  | OUSE | AI  | BL |
 +-----+------+-----+----+
 | MI  |  DO  | EON | SI |
 +-----+------+-----+----+
 | LIC |  MA  | NR  | EP |
 +-----+------+-----+----+
 | NG  |  UB  | NI  | YO |
 +-----+------+-----+----+
 | CA  | CILY | DU  | SE |
 +-----+------+-----+----+
(i) Top Beach Vacation Destination	D•••••••• R••••••• (9, 8)

(ii) European Region	S••••• (6)

(iii) Item of Clothing	b••••• (6)

(iv) Downstairs	d•••••• (7)

(v) Hamburger Ingredient	m••••••••• (10)

• Combine groups of letters to create words.
• Each clue has one word associated with it.
• "N letters" shows how many letters each answer has.