Prove Directly from the Definition of Congruence Modulo $n$ That If $a , c$

question 16

Essay

Prove directly from the definition of congruence modulo $n$ that if $a , c$ , and $n$ are integers, $n > 1$ , and $a \equiv c ( \bmod n )$ , then $a ^ { 3 } \equiv c ^ { 3 } ( \bmod n )$ .

Grasp the mathematical relationship between APC and APS, including understanding their inversely proportional nature.

Understand the factors influencing autonomous and induced consumption.

Identify the effects of interest rate changes on savings and consumption.

Recognize the significance of the marginal propensity to consume (MPC) and the marginal propensity to save (MPS).

---

Definitions:

Syndicate

A group of individuals or firms that join together to finance a project; also called an investment group.

Corporation

A legal entity that is separate from its owners, offering limited liability to its shareholders, and able to own property, enter contracts, and sue or be sued.

Partnership

A legal arrangement where two or more individuals share ownership of a business, including its liabilities and profits.

Cooperative

An association, which may or may not be incorporated, that is organized to provide an economic service to its members. Unincorporated cooperatives are often treated like partnerships for tax and other legal purposes.