Untitled - Purdue Math
... and y = 3x + 1. Give an answer accurate to within ±.01. (Note: If you were asked to find the area between these curves, you would need to find these points before integration. There is no algebraic way to solve for these points.) (17) Prove than any cubic polynomial f (x) = ax3 + bx2 + cx + d has at ...
... and y = 3x + 1. Give an answer accurate to within ±.01. (Note: If you were asked to find the area between these curves, you would need to find these points before integration. There is no algebraic way to solve for these points.) (17) Prove than any cubic polynomial f (x) = ax3 + bx2 + cx + d has at ...
There are infinitely many limit points of the fractional parts of powers
... |a0 | + |a1 | + · · · + |ad |. Suppose that ξ > 0 is a real number satisfying ξ ∈ / Q(α) in case α is a PV-number. Recall that an algebraic integer α > 1 is called a Salem number if its conjugates are all in the unit disc |z| ≤ 1 with at least one conjugate lying on |z| = 1. The next lemma is part o ...
... |a0 | + |a1 | + · · · + |ad |. Suppose that ξ > 0 is a real number satisfying ξ ∈ / Q(α) in case α is a PV-number. Recall that an algebraic integer α > 1 is called a Salem number if its conjugates are all in the unit disc |z| ≤ 1 with at least one conjugate lying on |z| = 1. The next lemma is part o ...
![[Part 1]](http://s1.studyres.com/store/data/008795717_1-da61206028950a8b76c72065c95ca070-300x300.png)
![arXiv:1003.5939v1 [math.CO] 30 Mar 2010](http://s1.studyres.com/store/data/016290525_1-37241e0159a202e5bf035fd4e5a48270-300x300.png)
Section 1.2-1.3
... In a proof of a statement (8n b) P (n) by mathematical induction, b is referred to as the base value. The proof of P (b) is called the base step and the proof of (8n b) [P (n) ! P (n + 1)] is called the inductive step. In the latter proof diagram of proof strategy 1.3.1, the assumption P (n) is call ...
... In a proof of a statement (8n b) P (n) by mathematical induction, b is referred to as the base value. The proof of P (b) is called the base step and the proof of (8n b) [P (n) ! P (n + 1)] is called the inductive step. In the latter proof diagram of proof strategy 1.3.1, the assumption P (n) is call ...
Elementary Number Theory
... Definition 1.1. We say that a divides b, denoted a | b, if b = na for some integer n. If a divides b, then b is said to be divisible by a. The number a is called a divisor (or factor ) of b, and b is called a multiple of a. Example 1.2. Since 5 × 7 = 35, we know that 5 | 35 and 7 | 35. The divisors ...
... Definition 1.1. We say that a divides b, denoted a | b, if b = na for some integer n. If a divides b, then b is said to be divisible by a. The number a is called a divisor (or factor ) of b, and b is called a multiple of a. Example 1.2. Since 5 × 7 = 35, we know that 5 | 35 and 7 | 35. The divisors ...
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. The cases n = 1 and n = 2 were known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The theretofore unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for ""most difficult mathematical problems"".