show that 8th power of any number is the form of 17m or 17m+1
Answers
Answered by
2
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.
Answered by
1
Answer:
ʜᴏᴩᴇ ꜱᴏ ɪᴛ ʜᴇʟᴩꜱ ᴜ ᴅᴇᴀʀ ꜰʀɪᴇɴᴅ
Attachments:
Similar questions