7⁶ⁿ - 6⁶ⁿ, where n is an integer > 0, is not divisible by,

Question: 7⁶ⁿ - 6⁶ⁿ, where n is an integer > 0, is not divisible by,

Solution:
7⁶ⁿ - 6⁶ⁿ
= 7⁶ - 6⁶
= (7³)² - (6³)²
= (7³ + 6³)(7³ - 6³)
= (343 - 216)(343 + 216)
= 127 × 559
= 127 × 13 × 43

Clearly, it is divisible by 127, 13, 559.