Number Theory

Computer Science Level 3

Find a 4 digit number represented as $\overline{abcd}$ which have the following property:

$\overline{abcd} = a^a + b^b + c^c + d^d$

Clarification: $a,b,c,d$ are not necessarily distinct

The answer is 3435.

2 solutions

Arkajyoti Banerjee
Apr 30, 2017

a = 1 #The first digit of a non-single digit number cannot be zero
while a<=9:
    b=0
    while b<=9:
        c=0
        while c<=9:
            d=1
            while d<=9:
                if 1000*a + 100*b + 10*c + d == a**a + b**b + c**c + d**d: #A number with 4 digits a,b,c,d can be written as 1000*a + 100*b + 10*c + d
                    print(1000*a + 100*b + 10*c + d)
                d += 1
            c += 1
        b += 1
    a += 1

Giorgio Coniglio
Aug 7, 2016

3435 = 3^3 + 4^4 + 3^3 + 5^5

Number Theory

The answer is 3435.

2 solutions

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