Well this is a nice problem too.

The number of Positive Primitive Pythagorean Triples under 100100 is 1616.But what is the number of Positive Primitive Pythagorean Triples under 10000!10000!.Can we derive a fomula?

Note by Sumukh Bansal
1 year, 6 months ago

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What do you mean by "under 100"?

What have you tried?

Pi Han Goh - 1 year, 6 months ago

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

Sumukh Bansal - 1 year, 6 months ago

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@Sumukh Bansal
Hint 1: Find the parametrization of these 3 integers.

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

Hint 3: How can we find the number of unordered positive integers (m,n)(m,n) such that m2+n2<100 m^2 + n^2 < 100 ?

Pi Han Goh - 1 year, 6 months ago

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@Pi Han Goh Which 3 integers?

Sumukh Bansal - 1 year, 6 months ago

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@Sumukh Bansal Pythagorean triplets consist of how many integers?

Pi Han Goh - 1 year, 6 months ago

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

Sumukh Bansal - 1 year, 6 months ago

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

Pi Han Goh - 1 year, 6 months ago

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

Sumukh Bansal - 1 year, 6 months ago

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

Pi Han Goh - 1 year, 6 months ago

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

Sumukh Bansal - 1 year, 6 months ago

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@Sumukh Bansal Let me rephrase Hint 1:

Do you know how to systematically construct Pythagoras triplets?

Pi Han Goh - 1 year, 6 months ago

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@Pi Han Goh Using Euler's Formula

Sumukh Bansal - 1 year, 6 months ago

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