Diophantine Equations (Problem 7, Version 2)

Algebra Level 2

Solve the equation n n + 1 = ( n + 1 ) n n^n + 1 = (n+1)^n


The answer is 1.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Since n = x n = x , n = x = 1 n = x = 1 as n = x ≥ 2 , n x + 1 ≠ ( n + 1 ) x n = x \geq 2, n^x + 1 \neq (n + 1)^x

So, therefore, the answer is 1 \fbox 1

0 Helpful 0 Interesting 0 Brilliant 4 Confused

But 1^1+1=2 and (1+1)^1=2?...

Peter van der Linden - 11 months, 3 weeks ago

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LaTeX, please!

A Former Brilliant Member - 11 months, 3 weeks ago

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