The rabbit (or Fibonacci) numbers form a sequence (a(1) = 1), 1, 2, 3, 5, 8,13,21,34,...,in which a(n)+2 =a(n+1) +a(n) for an y n=1,2,... . Find the greatest common divisor of the numbers a(100) and a(99).

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The value of a text extends beyond its content to include the origin of the information it contains. This origin can be rooted in significant events or the accomplishments of individuals. A text may serve as a record of an event, providing valuable documentation for future reference. It can also convey the achievements of notable individuals, whether they made groundbreaking discoveries or created influential works. It's important to note that the author of a text may not always be the person re

they hear about local and global phenomena and they want more complexity. So I think about mathematics. Local! Global! Whoa! Not that simple. Forget it. I will do what I always do. Present the analysis right when they need it. Too late to change. Pisses them off. Something really stylish this time. A masterpiece by Euler. You mean s-t-y-l-i-s-h. No... they're on to me. Gotta be something new or they won't buy it. I've been here before... that moment when your mind races for the concept... You ca

This brochure, written by Vladimir Arnold, consists of 77 problems for development of thinking culture, either selected or composed by the author. Most of them do not require any special knowledge beyond the general education. However, solving some of them may turn out challenging even for professors.

$De façon générale, cherchons une solution de : \[ dX_t = [a_1(t)X_t + a_0(t)]dt + [b_1(t)X_t + b_0(t)]dW_t, \quad X_0 \text{ donné} \] On commence par chercher une solution $F_t$ du système homogène: $dF_t = a_1(t)F_t dt + b_1(t)F_t dW_t$ avec $F_0 = 1$. Trivialement : \[ F_t = \exp\left[\int_0^t \left(a_1(s) - \frac{1}{2}b_1(s)^2\right)ds + \int_0^t b_1(s)dW_s\right] \] On va ensuite cherche une solution autour de $F_t$ en posant On pose $Y_t = X_t/F_t$ où par Itô : \[ d\left({1\over F$

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Hosea 1:6-9 (Lo-Ruhamah: "Not Loved," Lo-Ammi: "Not My People") Jeremiah 20:3 (Pashhur → "Terror on Every Side") These verses depict a god who withholds love and belonging, casting out those who do not conform. Jeremiah 20:3 "The next day, when Pashhur released him from the stocks, Jeremiah said to him, 'The Lord’s name for you is not Pashhur, but Terror on Every Side.'" Hosea 1:6-9 "Gomer conceived again and gave birth to a daughter. Then the Lord said to Hosea, 'Call her Lo-Ruhamah (which me

How many ways are there to break up the number 64 into 10 natural summands (integers ≥ 1), whose maximum is 12? [Ways that differ only by the order of their summands do not count as different.]

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