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666 is divisible by 666. 6×66\times66×6 is divisible by 6+66+66+6. 6×6×66\times6\times66×6×6 is divisible by 6+6+66+6+66+6+6.
Is it true that 6×6×⋯×6⏟n times\underbrace{6\times6\times\cdots\times6}_{n\text{ times}} n times6×6×⋯×6 is divisible by 6+6+⋯+6⏟n times\underbrace{6+6+\cdots+6}_{n\text{ times}} n times6+6+⋯+6 for all positive integers nnn?
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