Suppose for contradiction that there is a largest integer. Let this integer be n.

Prove by contradiction that there does not exist a largest integer. Hint: observe that for any integer n there is a greater one, say n+1. So begin the proof "Suppose for contradiction that there is a largest integer. Let this integer be n...."

Solving equation

Prove that y^2= x^3+23 has NO integer solutions.

Set Theory

1- prove : 1/2^2 + 1/3^2 +1/4^2+ ..... + 1/n^2 < 1

Quantitative methods review: definitions, probability, statistics, etc.

1. Match the terms with the definitions: a. Model b. Constraint c. Objective Function d. Uncontrolled input e. Probability f. Experiment g. Sample space h. Classical method i. Bayes Theorem j. Optimal solution k. Random variable l. Probability function m. Standard deviation n. Variance o. Independent events — A numerical measure of the likelihood that an event will occur. — The mathematical expression that defines the quantity to be maximized or minimized. — The set of all sample points (experimental outcomes). — The environmental factors or inputs that cannot be controlled by the decision maker. — A restriction or limitation imposed on a problem. ... click for more

Theory of Numbers

The Lucas numbers Ln are defined by the equations L1 = 1 and Ln = Fn+1 + Fn-1 for each n ≥ 2 Prove that Ln = Ln-1 + Ln-2 (n ≥ 3) See attached file for full problem description.