if p is prim number and p divides k२ then p divide
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Answer:
(a+b)
p
−a
p
−b
p
=[a
p
+
p
C
1
a
p−1
b+...+
p
C
p−1
ab
p−1
+
p
C
p
a
0
b
p
]−a
p
−b
p
=
p
C
1
a
p−1
b+...+
p
C
p−1
ab
p−1
=p(a
p−1
b)+
2
p(p−1)
a
p−2
b
2
+...+pab
p−1
=p((a
p−1
b)+
2
(p−1)
a
p−2
b
2
+...+ab
p−1
)
Hence the above expression is divisible by p.
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