Question

Find all solutions to:

Answer 1

\[x ^{n+1}-(x+1)^{n}=2001\]
in positive integers x,n.

Answer 2

@Yahoo!
@Australopithecus <-- Lucy?

Answer 3

@unkabogable

Answer 4

are u familiar with modular arithmetic ?

Answer 5

I never did well on the AMC anyway...

Answer 6

\[x^{n+1}-(x+1)^n+1=2002\]LHS is divisible by \(x\) so .. \(x\) must be a divisor of \(2002\)

Answer 7

I got it

Answer 8

taking mod \(3\) and mod \(x+1\) will be helpful...

only solution is \(x=13\) and \(n=2\)

Answer 9

yes