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In the five-digit base ten numeral ABCDE, different letters do not necessasrily represent different digits.  If this numeral is the fourth power of an integer and if  A + C + E = B + D, find the digit C.

 Dec 8, 2019
 #1
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The number is =14,641. It is = 11^4

 

A + C + E = B + D

 

1 + 6 + 1 = 4 + 4

 

8  =  8

 Dec 8, 2019
 #2
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In the five-digit base ten numeral ABCDE, different letters do not necessasrily represent different digits.  If this numeral is the fourth power of an integer and if  A + C + E = B + D, find the digit C.

 

10^4=10000    

17^4=83521

19^4 is too big.  so there are only  17-10+1= 8 possible numbers

 

Since there is only 8 possibilities I would just list them and see which one works for the given equation.

 Dec 8, 2019

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