Evaluate the following: (i) 7^1300 mod 8, (ii) 72^36 mod 15, (iii) 15^546 mod 17. You...
Evaluate the following: (i) 7^1300 mod 8, (ii) 72^36 mod 15,
(iii) 15^546 mod 17. You may not use a calculator or computer - do
this by hand, and show your computations.
Homework Answers
i. In order to calculate 7^1300 mod 8, which is equal to 49^650
mod 8 let us use the property that 
So,
Hence, 7^1300 mod 8 is 1.
ii. To solve 72^36 mod 15, let us use a very important property that
Hence, below is the series of steps of reduction
iii. Here in 15^546, let us use the property that 
So, 546 = 16*34 + 2
Hence,
Hence 4 is the answer.
Please comment for any clarification.
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