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# Introduction
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You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles.
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One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project.
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The letter reads:
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> Dear Mathematician,
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>
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> I need your help.
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> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c².
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> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N.
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> Calculating these triplets by hand would take me years, but I hear you are more than up to the task.
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>
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> Time is of the essence.
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> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem.
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Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition.
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Your work could have far-reaching implications, unlocking new possibilities in science and engineering.
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Can you rise to the challenge and make history?
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# Introduction
2+
3+
You are an accomplished problem-solver, known for your ability to tackle the most challenging mathematical puzzles.
4+
One evening, you receive an urgent letter from an inventor called the Triangle Tinkerer, who is working on a groundbreaking new project.
5+
The letter reads:
6+
7+
> Dear Mathematician,
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>
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> I need your help.
10+
> I am designing a device that relies on the unique properties of Pythagorean triplets — sets of three integers that satisfy the equation a² + b² = c².
11+
> This device will revolutionize navigation, but for it to work, I must program it with every possible triplet where the sum of a, b, and c equals a specific number, N.
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> Calculating these triplets by hand would take me years, but I hear you are more than up to the task.
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>
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> Time is of the essence.
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> The future of my invention — and perhaps even the future of mathematical innovation — rests on your ability to solve this problem.
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Motivated by the importance of the task, you set out to find all Pythagorean triplets that satisfy the condition.
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Your work could have far-reaching implications, unlocking new possibilities in science and engineering.
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Can you rise to the challenge and make history?

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