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
1 year, 10 months ago

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- 1 year, 10 months ago

What do you mean by "under 100"?

What have you tried?

- 1 year, 10 months ago

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

- 1 year, 10 months ago


Hint 1: Find the parametrization of these 3 integers.

Hint 2: Let $(a,b,c)$ be these 3 integers such that $a. 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 $m^2 + n^2 < 100$?

- 1 year, 10 months ago

Which 3 integers?

- 1 year, 10 months ago

Pythagorean triplets consist of how many integers?

- 1 year, 10 months ago

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

- 1 year, 10 months ago

There are infinitely many integers less than 100000!.

- 1 year, 10 months ago

So how can we select three integers?

- 1 year, 10 months ago

Have you worked through Hints 1 through 3?

- 1 year, 10 months ago

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

- 1 year, 10 months ago

Let me rephrase Hint 1:

Do you know how to systematically construct Pythagoras triplets?

- 1 year, 10 months ago

Using Euler's Formula

- 1 year, 10 months ago