Armstrong numbers are properly termed pluperfect digital invariant (PPDI) numbers. For an n-digit PPDI, the number is equal to the sum of each of its digits raised to the nth power. For example, for n = 3, there is 153 = 1^3 + 5^3 + 3^3 = 1 + 125 + 27. Incidentally, the mathematician G H Hardy stated that there are only four 3-digit PPDIs. He added that, although amusing, "there is nothing in them which appeals to the mathematician".
Armstrong numbers are apparently named after a computing lecturer at the University of Rochester named Michael F Armstrong. In the mid 1960s he devised Armstrong numbers as an exercise for his students.
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A number with n digits such that it is equal to the sum of the nth powers of its digits is called an n-Armstrong number. For example 1634 is a 4-Armstrong number because 14 + 64 + 34 + 44 = 1 + 1296 + 81 + 256 = 1634. There are 88 such numbers in base 10.
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The Armstrong numbers from 0 to 10000 are 1,153, 370, 371, 407!! That's it Nothing more and nothing less ;) Let k be the number of digits in a number, n, and d1,d2,d3,d4... be the digits of n. Say n=370. Then k=3 and d1=3, d2=7 and d3=0. Now 33+73+03=370. So 370 is an Armstrong number. Armstrong iff n=d1k+d2k+d3k+d4k+...