Question

find the remainder when 25^102 is divisible by 17
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Answer 1

Answer:4

Step-by-step explanation:

Using Fermat's Theorm,

R[(25^16)/17] = 1.

Now this can be extended to higher multiples of 16 as well i.e.

R[(25^16k)/17] = 1, where 16k is a multiple of 16.

The highest power of 16 less than 102 is 96. So we can take it out. So only 6 remains.

Now the task is as simple as

R[(25^6)/17] = R[((17+8)^6)/17] = R[(8^6)/17] = R[(512*512)/17 ] = 4.

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