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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, 6 months 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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`\boxed{123}`

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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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$100000!$

Thanks but to start we have to first find three integers less thanLog in to reply

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Do you know how to systematically construct Pythagoras triplets?

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