Question

By a Pythagorean triple we call a triple of positive integers a, b, c such that a2 + b2 = c2 and the integers a, b, c do not have a common prime factor. Using a formula for the stereographic projection find a Pythagorean triple a, b, c such that the product abc is divisible by 236. Please answer it right and clear.

Answer 1

To find a Pythagorean triple such that the product abc is divisible by 236, we can use the formula for the stereographic projection. Let's consider k = 1 and try different values of m and n until we find a triple that satisfies the condition. The Pythagorean triple that satisfies the condition is a = 3, b = 4, and c = 5.

Step-by-step explanation:

To find a Pythagorean triple such that the product abc is divisible by 236, we can use the formula for the stereographic projection. The formula is given as:

a = k * (m² - n²)

b = k * (2mn)

c = k * (m² + n²)

where k, m, and n are positive integers, with m > n. We need to find values of m, n, and k such that the product abc is divisible by 236.

Let's consider k = 1 and try different values of m and n until we find a triple that satisfies the condition. We start with m = 2 and n = 1:

a = 3

b = 4

c = 5

abc = 3 * 4 * 5 = 60

Since 60 is divisible by 236, this is a valid Pythagorean triple.

So, the Pythagorean triple that satisfies the condition is a = 3, b = 4, and c = 5.