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Prove or Disprove: for All Integers A, B, C, D (a+c)(b+d)( a + c ) \mid ( b + d )

question 109

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Prove or disprove: For all integers a, b, c, d, if a|b and c|d, then (a+c)(b+d)( a + c ) \mid ( b + d )


Definitions:

Purchase

Purchase involves the act of acquiring goods or services in exchange for money, representing a basic transaction in the economic system.

Commission

A fee paid to an agent or employee for transacting a piece of business or performing a service.

Purchasing Power

The real value of money, reflecting how much goods or services one unit of money can buy.

Period

A length or portion of time, often defined for specific calculations or measurements.

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