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The number of Positive Primitive Pythagorean Triples under \(100\) is \(16\).But what is the number of Positive Primitive Pythagorean Triples under \(10000!\).Can we derive a fomula?

Note by Sumukh Bansal 1 year, 1 month ago

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@Pi Han Goh @Jon Haussmann @Brian Charlesworth @Brandon Monsen @Sharky Kesa @Otto Bretscher any help

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What do you mean by "under 100"?

What have you tried?

By under 100 I mean the positive integers less than 100.

@Sumukh Bansal – \(\) Hint 1: Find the parametrization of these 3 integers.

Hint 2: Let \((a,b,c) \) be these 3 integers such that \(a<b<c\). Prove that the parities of \(a\) and \(b\) are distinct.

Hint 3: How can we find the number of unordered positive integers \((m,n) \) such that \( m^2 + n^2 < 100 \)?

@Pi Han Goh – Which 3 integers?

@Sumukh Bansal – Pythagorean triplets consist of how many integers?

@Pi Han Goh – Thanks but to start we have to first find three integers less than \(100000!\)

@Sumukh Bansal – There are infinitely many integers less than 100000!.

@Pi Han Goh – So how can we select three integers?

@Sumukh Bansal – Have you worked through Hints 1 through 3?

@Pi Han Goh – Nope I don't know how to get started I mean select 3 integers

@Sumukh Bansal – Let me rephrase Hint 1:

Do you know how to systematically construct Pythagoras triplets?

@Pi Han Goh – Using Euler's Formula

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TopNewest@Pi Han Goh @Jon Haussmann @Brian Charlesworth @Brandon Monsen @Sharky Kesa @Otto Bretscher any help

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What do you mean by "under 100"?

What have you tried?

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By under 100 I mean the positive integers less than 100.

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Hint 1:Find the parametrization of these 3 integers.Hint 2:Let \((a,b,c) \) be these 3 integers such that \(a<b<c\). Prove that the parities of \(a\) and \(b\) are distinct.Hint 3:How can we find the number of unordered positive integers \((m,n) \) such that \( m^2 + n^2 < 100 \)?Log in to reply

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Do you know how to systematically construct Pythagoras triplets?

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