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1 If n is a natural number and n ≥ 2, then (2n, n²-1, n²+1) is a Pythagorean triple.

1 If n is a natural number and n ≥ 2, then (2n, n²-1, n²+1) is a Pythagorean triple.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Either prove or disprove this mathematical claim detailed please
problems use Pythagorean Theorem, assumed to be true without any proof: "For any right triangle, if its legs have length a and b and its hypotenuse length c, then a² + b² c²." In addition, two additional definitions are relevant to the conjectures you choose from below: a Pythagorean triple (p, q, r) is a triple of natural numbers p <q <r such that p²+q² = r². An equilateral triangle is one for which all three sides have equal length. 1 If n is a natural number and n ≥ 2, then (2n, n² − 1, n²+1) is a Pythagorean triple.
Transcribed Image Text:problems use Pythagorean Theorem, assumed to be true without any proof: "For any right triangle, if its legs have length a and b and its hypotenuse length c, then a² + b² c²." In addition, two additional definitions are relevant to the conjectures you choose from below: a Pythagorean triple (p, q, r) is a triple of natural numbers p <q <r such that p²+q² = r². An equilateral triangle is one for which all three sides have equal length. 1 If n is a natural number and n ≥ 2, then (2n, n² − 1, n²+1) is a Pythagorean triple.
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