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 $a ^ { 3 } \equiv c ^ { 3 } ( \bmod n )$ .

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Definitions:

Hypothesis Testing

A statistical method that is used in making statistical decisions using experimental data.

Specific Hypotheses

Precise, testable predictions derived from a broader theory that specify the expected relationship between variables.

Cognitive Dissonance

A psychological state in which an individual experiences discomfort due to holding contradictory beliefs or attitudes, often leading to an alteration in one of the conflicting cognitions.

Mid-Level

Pertains to a position, status, or area that is in between the highest and the lowest levels, often implying a moderate degree of complexity or authority.