# 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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- 7 months, 2 weeks ago

What do you mean by "under 100"?

What have you tried?

- 7 months, 2 weeks ago

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

- 7 months, 2 weeks ago


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 $$m^2 + n^2 < 100$$?

- 7 months, 2 weeks ago

Which 3 integers?

- 7 months, 2 weeks ago

Pythagorean triplets consist of how many integers?

- 7 months, 2 weeks ago

Thanks but to start we have to first find three integers less than $$100000!$$

- 7 months, 2 weeks ago

There are infinitely many integers less than 100000!.

- 7 months, 2 weeks ago

So how can we select three integers?

- 7 months, 2 weeks ago

Have you worked through Hints 1 through 3?

- 7 months, 2 weeks ago

Nope I don't know how to get started I mean select 3 integers

- 7 months, 2 weeks ago

Let me rephrase Hint 1:

Do you know how to systematically construct Pythagoras triplets?

- 7 months, 2 weeks ago

Using Euler's Formula

- 7 months, 1 week ago