Teaching NVS TGT 2024 Test Series Mathematics Elementary Number Theory Congruence

If 'p' is a prime, then the congruence x² + 1 ≡ 0 (mod p) has a solution if and only if:

1

p = 1 or p ≡ 1 (mod 3)

2

p ≠ 1 or p ≡ 1 (mod 2)

3

p = 2 or p ≡ 1 (mod 4)

4

p = -2 or p ≡ 2 (mod 3)

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