Question

show that 8th power of any number is the form of 17m or 17m+1​

Answer 1

Answer:

If N is prime to 17 then

by using Femats little theorem if p is a prime number and N is prime to p then N

p−1

−1 is a multiple of p

Put p=17

⇒N

17−1

−1=17n

⇒N

16

−1=17n

⇒(N

8

)

2

−1

2

=17n

⇒(N

8

+1)(N

8

−1)=17n

⇒N

8

=17n±1

If N is not prime to 17 then obviously

N

8

=17n

Hence proved.

Answer 2

Answer:

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