Question

if p is prim number and p divides k२ then p divide
​

Answer 1

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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