Is any Armstrong number above 1000?

Answer 1

No, because according to one definition, an Armstrong number can have only three digits.

Armstrong numbers belong to a class of numbers, called Narcissistic numbers. A Narcissistic number of n digits must equal the sum of the nth power of its digits.

So, the smallest 4-digit Narcissistic number is 1634 = 1^4 + 6^4 + 3^4 + 4^4.

The largest Narcissistic number is the 39-digit numbers:

115132219018763992565095597973971522401.

It has been proved, by D Winter in 1985, that there can be no larger Narcissistic number in base 10 arithmetic.