Minimum Sum of Non-Negative Integers with Given Equation - POTW #504

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In summary, the "Minimum Sum of Non-Negative Integers with Given Equation" problem is a mathematical problem that involves finding the minimum sum of non-negative integers that satisfy a given equation. It is important for developing problem-solving skills and has practical applications in computer science and engineering. There are several common approaches to solving this problem, including brute force, dynamic programming, and greedy algorithm. To improve skills in solving this problem, one can practice and study different approaches and algorithms, as well as participate in coding competitions. While the problem can be solved for most equations, there are some cases where no solution exists.
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anemone
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Here is this week's POTW:

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Let ##a,\,b,\,c## and ##d## be non-negative integers.

If ##a^2+b^2-cd^2=2022##, find the minimum of ##a+b+c+d##.

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Thanks for the interesting problem. I have not found the answer but I would like to guess it.
[tex]s:=a+b+c+d=a+b+d+\frac{a^2+b^2-2022}{d^2}[/tex]
Guessing for minimum s that a=b and ##2a^2-2022## is least with an integer c
[tex]a=b=32, d=1, c=26[/tex]
[tex] s=91[/tex]
A nearby case is
[tex]a=33,b=31,d=1,c=28;\ s=93>91[/tex]
However, for a>>b case
[tex]a=45,b=1,d=2,c=1;\ s=49 [/tex]
My guess failed. I will be glad to know the right answer.
 
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Related to Minimum Sum of Non-Negative Integers with Given Equation - POTW #504

1. What is the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem?

The "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem is a mathematical puzzle that was featured as a "Problem of the Week" on a popular online platform. It involves finding the smallest possible sum of non-negative integers that satisfies a given equation.

2. What is the equation used in the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem?

The equation used in the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem is a linear equation of the form ax + by = c, where a, b, and c are given constants and x and y are non-negative integers.

3. How do you solve the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem?

To solve the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem, you can use a systematic approach by trying different combinations of non-negative integers for x and y until you find a solution that satisfies the given equation. You can also use algebraic methods and number properties to simplify the equation and find a solution.

4. Is there a unique solution to the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem?

No, there may be multiple solutions to the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem. However, there is always a smallest possible sum of non-negative integers that satisfies the given equation, which is the main objective of the problem.

5. What is the significance of the "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem?

The "Minimum Sum of Non-Negative Integers with Given Equation - POTW #504" problem is a fun and challenging mathematical puzzle that helps develop problem-solving and critical thinking skills. It also has practical applications in fields such as computer science, engineering, and economics.

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