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find the number of solutions in z103
x^2==22(mod103)
x^2==22(mod103)
A solution in this context refers to a number that, when squared, is equivalent to 22 modulo 103 in the set of integers modulo 103 (also known as Z103).
In the set of integers modulo 103, there are either two solutions or no solutions to this equation. This is because the set of integers modulo 103 has a total of 103 elements, and for any given number, there can only be two possible square roots modulo 103.
There are a few methods for finding solutions to this equation in Z103. One approach is to use trial and error, plugging in different numbers and checking if their square is equivalent to 22 modulo 103. Another method is to use modular arithmetic and algebraic manipulation to simplify the equation and find the solutions.
No, there can only be a maximum of two solutions for a given number in Z103. This is because of the nature of modular arithmetic - for any given number, there can only be two possible square roots modulo 103.
Yes, instead of using the set of integers modulo 103, the solutions to this equation can also be represented using congruence notation. For example, if x is a solution, then x ≡ ± √22 (mod 103). This notation indicates that x is equivalent to either the positive or negative square root of 22 modulo 103.