Pythagorean triplets

Geometry Level 3

Read the following statements

  • 1) \(n, n+1\) are two consecutive positive integers. A Pythagorean triplet can be formed, if \( n\) and \(n+1\) are the two sides of the Right angled triangle(excluding hypotenuse).

  • 2) \(n, n+10\) are two integers(\(n\) being a positive integer).A Pythagorean triplet can be formed, if \(n\) and \(n+10\) are the two sides of the Right angled triangle(excluding hypotenuse).

  • 3) \(n, n+30\) are two positive integers(\(n\) being a positive integer). A Pythagorean triplet can be formed, if \(n\) and \(n+30\) are the two sides of the Right angled triangle(excluding hypotenuse).

Which of the above statements are true?

Clarification: A Pythagorean triplet is a set of three integers which satisfy the pythagorean theorem.

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