Well this is a nice problem too.

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
7 months, 2 weeks ago

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What do you mean by "under 100"?

What have you tried?

Pi Han Goh - 7 months, 2 weeks ago

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

Sumukh Bansal - 7 months, 2 weeks ago

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@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 - 7 months, 2 weeks ago

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@Pi Han Goh Which 3 integers?

Sumukh Bansal - 7 months, 2 weeks ago

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@Sumukh Bansal Pythagorean triplets consist of how many integers?

Pi Han Goh - 7 months, 2 weeks ago

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

Sumukh Bansal - 7 months, 2 weeks ago

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

Pi Han Goh - 7 months, 2 weeks ago

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

Sumukh Bansal - 7 months, 2 weeks ago

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

Pi Han Goh - 7 months, 2 weeks ago

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

Sumukh Bansal - 7 months, 2 weeks ago

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@Sumukh Bansal Let me rephrase Hint 1:

Do you know how to systematically construct Pythagoras triplets?

Pi Han Goh - 7 months, 2 weeks ago

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@Pi Han Goh Using Euler's Formula

Sumukh Bansal - 7 months, 1 week ago

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