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What is the sum of the final three digits of the integer representation of 5^100?

 Jul 6, 2019
 #1
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Note the pattern 

5^1  = 5

5^2 = 25

5^3 = 125

5^4  = 625

5^5 = 3125

5^6 = 15625

5^7 = 78125

5^8 = 390625

 

So...it appears that  for n ≥ 2,   5^(2n)  will end in ....625

 

So....5^(2 * 50)   = 5^100   ends in 625

 

And the sum is  6 + 2 + 5  =   13

 

 

cool cool cool

 Jul 6, 2019

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