ANSWERS: 2
  • Um, I'm not sure what you mean but 5 to the power of 2 equals 25. 4 to the power of 2 equals 16 and 3 to the power of 2 equals 9 25 = 16 + 9 I'm not sure what you mean though in your question. If you're suggesting that n^2 = (n-1)^2 + (n-2)^2, where n is an integer greater than 5, I'm not sure if that is true but you could probably google it to find out.
  • Just luck: those are the first Pythagorean triples: "Pythagorean triples Main article: Pythagorean triple A Pythagorean triple has three positive integers a, b, and c, such that a^2 + b^2 = c^2. In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. Evidence from megalithic monuments on the Northern Europe shows that such triples were known before the discovery of writing. Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13). List of primitive Pythagorean triples up to 100 (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), (11, 60, 61), (12, 35, 37), (13, 84, 85), (16, 63, 65), (20, 21, 29), (28, 45, 53), (33, 56, 65), (36, 77, 85), (39, 80, 89), (48, 55, 73), (65, 72, 97)" Source and further information: http://en.wikipedia.org/wiki/Pythagorean_Theorem#Pythagorean_triples Further information: http://en.wikipedia.org/wiki/Pythagorean_triple

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