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Let [a, b, c] be a primitive triple with a odd. Then 3 new triples [a 1, b 1, c 1], [a 2, b 2, c 2], [a 3, b 3, c 3] may be produced from [a, b, c] using matrix multiplication and Berggren's [11] three matrices A, B, C. Triple [a, b, c] is termed the parent of the three new triples (the children). Each child is itself the parent of 3 more ...
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
Galileo's law of odd numbers. A ramification of the difference of consecutive squares, Galileo's law of odd numbers states that the distance covered by an object falling without resistance in uniform gravity in successive equal time intervals is linearly proportional to the odd numbers. That is, if a body falling from rest covers a certain ...
In mathematics, an interprime is the average of two consecutive odd primes. [1] For example, 9 is an interprime because it is the average of 7 and 11. The first interprimes are:
For example, consider the sum: 2 + 5 + 8 + 11 + 14 = 40 {\displaystyle 2+5+8+11+14=40} This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2:
Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. [2] Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That ...