PDF-Applications of Fermats Little Theorem and Congruences

Then integers and are congruent modulo m denoted by mod m if Example 1 mod 2 4 mod 2 14 0 mod 7 25 16 mod 9 43 27 mod 35 Properties Let be a positive integer and let abcd be integers Then 1 mod 2 If mod m then mod m 3 If mod and mod m then mod m 4 a. Let IR be a continuous function and IR IN be a sequence of continuous functions If IN converges pointwise to and if 1 for all and all IN then IN converges uniformly to Proof Set for each IN Then IN is a sequence of continuous functions on the co Then there exists a number in ab such that The idea behind the Intermediate Value Theorem is When we have two points af and bf connected by a continuous curve The curve is the function which is Continuous on the interval ab and is a numb If am 1 then the congruence ax mod phas exactly one solution modulo Constructive Solve the linear system sa tm 1 Then sba tbm b So sba mod gives the solution sb If and are solutions then au mod and au mod au au mod mod since a Chen Dan Dong. Feb. 19, 2013. Outline. Review of asymptotic notations. Understand the Master Theorem. Prove the theorem. Examples and applications. Review of Asymptotic Notation. Θ. notation. : asymptotic tight bound. Learner Objective: Students will apply a Right Angle Theorem as a way of proving 
 that two angles are right angles and to solve problems involving right angles.. Advanced Geometry. Learner Objective: Students will apply a Right Angle Theorem as a way of proving 
 that two angles are right angles and to solve problems involving right angles.. . . . . by . Changqing. Li. Mathematics. Discrete geometry. Computational geometry. Measure theory. What is “ham sandwich theorem”?. The volumes of any . Section 9.3b. Remainder Estimation Theorem. In the last class, we proved the convergence to a Taylor. s. eries to its generating function (sin(. x. )), and yet we did. n. ot need to find any actual values for the derivatives of. Rolle’s. theorem. Exploration:. Sketch a rectangular coordinate plane on a piece of paper.. Label the points (1, 3) and (5, 3).. Draw the graph of a differentiable function that starts at (1, 3) and ends at (5, 3).. By Katherine Voorhees. Russell Sage College. April 6, 2013. A Theorem of Newton. Application and significance . A Theorem of Newton derives a relationship between the roots and the coefficients of a polynomial without regard to negative signs.. “. REVERSE. ”. . probability theorem. The . “. General. ”. Situation. A sample space S is . “. broken up. ”. into chunks . Well, maybe N chunks, not just 4.. This is called a . “. PARTITION. 2. B. 2 . = C. 2. THE PYTHAGOREAN THEOREM. LEG A. LEG B. HYPOTENUSE. PARTS OF A RIGHT TRIANGLE. THE PYTHAGOREAN THEOREM. DIAGONALS. SIDES. PARTS OF A RECTANGLE. OR SQUARE. SIDES. NOTICE TWO RIGHT TRIANGLES FORM A RECTANGLE. Presenter: Tianyi Shan. 1. Organization. Motivation and background. The “SNOW” theorem. COPS-SNOW design and Rococo-SNOW design. Evaluation of the results. Takeaway and Discussion. 2. Motivation and background. Complex Numbers. Standard form of a complex number is: . a bi.. Every complex polynomial function of degree 1 or larger (no negative integers as exponents) has at least one complex zero.. a . and. b . 4. 3. 2. 1. 0. In addition to level 3.0 and beyond what was taught in class, the student may. : . Make connection with other concepts in math.. Make connection with other content areas.. Explain the relationship between the Pythagorean Theorem and the distance formula..