This equation is a congruence equation, meaning it is a way to express equivalence between two numbers. The "mod" in the equation stands for modulus, which represents the remainder when dividing by the number after it. In this case, the equation is stating that when you divide X^2 + 1 by 5^3, the remainder is 0.
The solution to this equation is any value of X that satisfies the congruence relationship with 0 when divided by 5^3. In other words, any X value that when squared and added to 1, is a multiple of 5^3, or 125.
Yes, this equation can have multiple solutions. Since the modulus is 5^3, there are 125 possible remainders when dividing by 5^3, and each of these remainders can be a solution to the equation.
This equation can be solved by substituting different values for X and checking if the resulting expression is a multiple of 5^3. Another way to solve it is by using modular arithmetic, where you manipulate the equation to isolate X and find a solution that satisfies the congruence relationship.
The "mod 5^3" in this equation is the modulus, which determines the range of possible solutions. In this case, the modulus 5^3 means that the solutions will be multiples of 125. It also allows for a finite number of solutions, as there are only 125 possible remainders when dividing by 5^3.