For an odd prime p, x²=-1(mod p) if and only if p=1(mod 4)| Tamil

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X square plus1congruent 0(mod p), p odd prime, has sol.if and only if p congr. 1(mod 4).(ANT53.HRB) X square plus1congruent 0(mod p), p odd prime, has sol.if and only if p congr. 1(mod 4).(ANT53.HRB)
x^2+1=0 (mod p) where p is prime has a solution iff p=1 (mod 4) _ x^2+1=0 (mod p) where p is prime has a solution iff p=1 (mod 4) _
Let p be an odd prime with p=3(mod 4). Then [(p-1/2)!]²=1(mod p) Let p be an odd prime with p=3(mod 4). Then [(p-1/2)!]²=1(mod p)
if p is an odd prime prove that(-z/p)={1 if p=1mod8 or p=3(mod 8) #hpu #lovemaths if p is an odd prime prove that(-z/p)={1 if p=1mod8 or p=3(mod 8) #hpu #lovemaths
1ᵖ⁻¹ + 2ᵖ⁻¹ + 3ᵖ⁻¹ +.............+ (p- 1)ᵖ⁻¹ ≡ - 1 (mod p) . proof , p is an odd prime number . 1ᵖ⁻¹ + 2ᵖ⁻¹ + 3ᵖ⁻¹ +.............+ (p- 1)ᵖ⁻¹ ≡ - 1 (mod p) . proof , p is an odd prime number .
Show that if p is an odd prime and 𝑟 is a primitive root 𝑚𝑜𝑑 𝑝 then 𝑥^2≡𝑟 𝑚𝑜𝑑 𝑝 has no solution Show that if p is an odd prime and 𝑟 is a primitive root 𝑚𝑜𝑑 𝑝 then 𝑥^2≡𝑟 𝑚𝑜𝑑 𝑝 has no solution
If p is an odd prime then find the number of solutions of x^(p-2)=1 If p is an odd prime then find the number of solutions of x^(p-2)=1
Employ Fermat Employ Fermat's Theorem to prove that, if p is an odd prime, then 1^(p-1)+...+(p-1)^(p-1)=-1(mod p)