Employ Fermat's Theorem to prove that, if p is an odd prime, then 1^(p-1)+...+(p-1)^(p-1)=-1(mod p)

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(Lecture 48) Theorem: p is prime iff phi(p)=p-1

1ᵖ⁻¹ + 2ᵖ⁻¹ + 3ᵖ⁻¹ +.............+ (p- 1)ᵖ⁻¹ ≡ - 1 (mod p) . proof , p is an odd prime number .

p^q=p (mod pq) - Fermat's Medium Sized Theorem

Wilson's theorem || If p is prime (p-1)! congruence 1 (mod p)

if p is an odd prime prove that(-z/p)={1 if p=1mod8 or p=3(mod 8) #hpu #lovemaths

Number theory example|if p is an odd prime prove that (2.3.4.5......)^2 is cong to (-1)^(p+1)/2 modp

Wilson's Theorem: If p is a prime no,then (p-1)!/p = p-1 or -1

If P is prime find x if 1^(p-1)+2^(p-1)+3^(p-1)+ + p-1^(p-1)=x(modp) then x=