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buzzmath
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How would i go about solving the problem of for which values of a is the congruence ax^4≡2(mod 13) solvable? I think it might have something to do with power residues but I'm not sure.
Thanks
Thanks
I would first find all values of x^2 mod 13 for x = 1 to 6 since the possible values just repeat for x > 6. For x = 1,2 and 4 they are 1,4 and 3, respectively. For x = 3,5 and 6 they are -4, -1 and -3. Squaring those values give just three possible values of x^4, i.e., 1,9,3 having respective [tex]a[/tex] values of 2, 6 and 5.buzzmath said:How would i go about solving the problem of for which values of a is the congruence ax^4≡2(mod 13) solvable? I think it might have something to do with power residues but I'm not sure.
Thanks
An index arithmetic problem is a type of mathematical problem that involves solving for the power or exponent in an equation. In this case, we are solving for the value of x in the equation ax^4≡2 (mod 13).
The goal of solving an index arithmetic problem is to find the value of the unknown variable (in this case, x) that satisfies the given equation. This allows us to solve for unknown quantities and understand the relationships between different variables in a mathematical expression.
To solve an index arithmetic problem, we use mathematical operations such as addition, subtraction, multiplication, and division to manipulate the equation until we isolate the unknown variable. In this case, we can use the properties of modular arithmetic to simplify the equation and find the value of x.
The "mod" in the equation ax^4≡2 (mod 13) stands for the modulo operation, which is a mathematical operation that calculates the remainder when one number is divided by another. In this case, we are looking for the value of x that satisfies the equation when it is divided by 13.
Solving index arithmetic problems is important because it allows us to solve for unknown quantities and understand the relationships between different variables in a mathematical expression. This is essential in many fields, including science, engineering, and economics, where mathematical equations are used to model and solve real-world problems.