3.23. Technique. (a) Use the Euclidean Algorithm to find a member x of the canonical complete residue system (mod 213) that satisfies 24 x≡ 123 (mod 213).

3.23. Technique. (a) Use the Euclidean Algorithm to findamemberxof the canonical complete residue system (mod213) that satisfies 24 x≡123 (mod213).

The problems in this chapter examine some variations on the apartment market described in the text. In most of the problems we work with the true demand curve constructed from the reservation prices of the

'I **Suppose**' ( oimai ): The Conclusion of John's Gospel in Its Literary and Historical Context Andreas J. Köstenberger Introduction Discussions of the authorship of the Fourth Gospel continue unabated, and commentators leave no stone unturned in their quest to solve this enigma of Johannine studies.

60 CHAPTER 9 9-1. **Suppose** a worker with an annual discount rate of 10 percent currently resides in Pennsylvania and is deciding whether to remain there or to move to Illinois.

People are told that our various wars were fought to make the world safe for democracy. But unsafe conditions still prevail. Individuals and groups keep seizing unfair advantages to the detriment of others who keep trying to fight back by doing the same thing.

29 CHAPTER 5 5-1. **Suppose** the labor supply curve is upward sloping and the labor demand curve is downward sloping. The study of economic trends over a particular time period reveals that the wage recently fell while employment levels rose.

Claim: There are infinitely many prime numbers. Proof. **Suppose**, to the contrary, that there are a finite number of prime numbers. Let p 1, p 2, p 3, …, p k be the entire collection of prime numbers.

proof. The basic idea is that ifx § 9 Limit Theorems for Sequences The theorems of this section allow complicated limits to be evaluated more easily.

Exercises for Day 8: Vector Fields 1. Change of Variables. **Suppose** that(V,φ)and(V,ψ)arecoordinatecharts onthe n-manifoldM and that φ =(x i) while ψ =(y