Given three positive integers a, b and c such that a² + b² - c² = 1. Let the number of triangles formed with sides a, b and c with perimeter less than 50 million represent the surface area of an ellipsoid of axes lengths n, 2n and 3n. The password is the square of the ceiled positive solution of n.

Question

Aarav Bernard

Mathematics

7 April, 02:29

Given three positive integers a, b and c such that a² + b² - c² = 1. Let the number of triangles formed with sides a, b and c with perimeter less than 50 million represent the surface area of an ellipsoid of axes lengths n, 2n and 3n. The password is the square of the ceiled positive solution of n.

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Answers (1)

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Billy Mueller · Answer 1

Step-by-step explanation:

Count pairs (a, b) whose sum of squares is N (a^2 + b^2 = N)

Given a number N, the task is to count all 'a' and 'b' that satisfy the condition a^2 + b^2 = N.

Note: - (a, b) and (b, a) are to be considered as two different pairs and (a, a) is also valid and to be considered only one time.

Examples:

Input: N = 10

Output: 2

1^2 + 3^2 = 9

3^2 + 1^2 = 9

Input: N = 8

Output: 1

2^2 + 2^2 = 8