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When the expression (7^1)(7^2)(7^3) ... (7^100) is written as an integer, what is the product of the tens digit and the ones digit?

 Feb 8, 2022
 #1
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To find the power of the full expression, we can find the sum of the numbers from 1-100. So, using the Gauss Formula:

 

n(n+1)/2

100(101)/2

10100/2

5050

 

We can then find patterns, since we are trying to find the tens and ones digits.

 

7^1 = 07

7^2 = 49

7^3 = 343

7^4 = 2401

7^5 = 16807

7^6 = 11649

7^7 = 823543

 

Use the pattern to solve the answer. Hope this helps!

 

Let me know if I did anything wrong!

 Feb 8, 2022
 #2
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productfor(n, 1, 70, 7^n) mod 10^10==8653632807 - these are the last 10 digits

 

7  x  0  ==0

 Feb 8, 2022

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