### How do you find the solution of quadratic congruence?

## How do you find the solution of quadratic congruence?

Thus , the congruence X2≡ ��(������ p) has exactly two solutions. The Quadratic congruence in one variable is given by ax2+bx+c ≡0(mod p) can be reduced to the form y2≡ d(mod p),where y=2ax+b & d=b2-4ac. From (1) we have a=1,b=3,c=11 , Y=2ax+b so the value of Y=2x+3, d=b2-4ac=32-4.11=-35.

### How do you solve quadratic residues?

We only need to solve, when a number (b) has a square root modulo p, to solve quadratic equations modulo p. Given a number a, s.t., gcd(a, p) = 1; a is called a quadratic residue if x2 = a mod p has a solution otherwise it is called a quadratic non-residue.

#### How do you solve quadratic variables?

Solving Quadratic Equations

- Put all terms on one side of the equal sign, leaving zero on the other side.
- Factor.
- Set each factor equal to zero.
- Solve each of these equations.
- Check by inserting your answer in the original equation.

**What are the solutions of quadratic equations?**

The “solutions” to the Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph). Just plug in the values of a, b and c, and do the calculations. We will look at this method in more detail now.

**How many solutions does a quadratic congruence have?**

two solutions

Solving the quadratic congruence x2 ≡ a (mod m) p odd: If a(p-1)/2 ≡ 1 (mod p), there are two solutions (mod pn).

## Is 0 a quadratic residue?

Modulo 2, every integer is a quadratic residue. Modulo an odd prime number p there are (p + 1)/2 residues (including 0) and (p − 1)/2 nonresidues, by Euler’s criterion. In this case, it is customary to consider 0 as a special case and work within the multiplicative group of nonzero elements of the field Z/pZ.

### For which primes p is 13 a quadratic residue?

For example when p = 13 we may take g = 2, so g2 = 4 with successive powers 1,4,3,12,9,10 (mod 13). These are the quadratic residues; to get the quadratic nonresidues multiply them by g = 2 to get the odd powers 2,8,6,11,5,7 (mod 13).

#### For which primes p is 5 a quadratic residue modulo p?

Law of quadratic reciprocity

a | a is a quadratic residue mod p if and only if |
---|---|

4 | (every prime p) |

5 | p ≡ 1, 4 (mod 5) |

6 | p ≡ 1, 5, 19, 23 (mod 24) |

7 | p ≡ 1, 3, 9, 19, 25, 27 (mod 28) |

**What is a quadratic model?**

A mathematical model represented by a quadratic equation such as Y = aX2 + bX + c, or by a system of quadratic equations. The relationship between the variables in a quadratic equation is a parabola when plotted on a graph. Compare linear model.

How do you find the solution of quadratic congruence? Thus , the congruence X2≡ ��(������ p) has exactly two solutions. The Quadratic congruence in one variable is given by ax2+bx+c ≡0(mod p) can be reduced to the form y2≡ d(mod p),where y=2ax+b & d=b2-4ac. From (1) we have a=1,b=3,c=11 , Y=2ax+b so the value of…