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Every prime number p divides a Fibonacci number that can be determined by the value of p modulo 5. If p is congruent to 1 or 4 modulo 5, then p divides F p−1, and if p is congruent to 2 or 3 modulo 5, then, p divides F p+1. The remaining case is that p = 5, and in this case p divides F p.
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
The 4–1–3–2 is a variation of the 4–1–2–1–2 and features a strong and talented defensive centre midfielder. This allows the remaining three midfielders to play further forward and more aggressively, and also allows them to pass back to their defensive mid when setting up a play or recovering from a counterattack.
The most common derivative of 1,3,5-triazine is 1,3,5-triazine-2,4,6-triamine, commonly known as melamine or cyanuramide. Another important derivative is 1,3,5-triazine-2,4,6-triol better known as cyanuric acid. Cyanuric chloride (2,4,6-trichloro-1,3,5-triazine) is the starting point for the manufacture of many herbicides such as Simazine and ...
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
Straight-five engines typically use a firing order of 1-2-4-5-3, in order to minimise the primary vibration from the rocking couple. Straight-six engines typically use a firing order of 1-5-3-6-2-4, which results in perfect primary and secondary balance. However, a firing order of 1-2-4-6-5-3 is common on medium-speed marine engines.
Illustration of the poem from the 1901 Book of Nursery Rhymes. This is one of many counting-out rhymes. It was first recorded in Mother Goose's Melody around 1765. Like most versions until the late 19th century, it had only the first stanza and dealt with a hare, not a fish, with the words: