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Find the remainder  is divided by 7. 

 

 

 

 

 

 

 

\($100^{100}$\)

 Jul 25, 2020
 #1
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Since you don't specify base b, that means the answer will be the same in any base from 2 to 10:

 

11011_2 * (2 - 1) + 1001 = 100100 = 36_10

11011_3 * (3 - 1) + 1001 = 100100 = 252_10

11011_4 * (4 - 1) + 1001 = 100100 = 1040_10

11011_5 * (5 - 1) + 1001 = 100100 = 3150_10

11011_6 * (6 - 1) + 1001 = 100100 = 7812_10

11011_7 * (7 - 1) + 1001 = 100100 = 16856_10

11011_8 * (8 - 1) + 1001 = 100100 = 32832_10

11011_9 * (9 - 1) + 1001 = 100100 = 59130_10

11011_10*(10-1) + 1001 = 100100 = 100100_10 

 Jul 25, 2020
 #2
avatar+110758 
+1

100^100    mod 7

 

=  (100mod7)^100   mod 7

=  2^100                   mod 7

=  2^(3*33)  *2          mod 7

=  (2^3)^33   *2         mod 7

=  1^33   *2               mod 7

=  2

 

I am assuming base 10

 Jul 25, 2020

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