If and where , prove that .
To prove: If and , where , then .
and , where .
i) Definition: Congruence Modulo
Let be a positive integer, . For integers and , is congruent to modulo , if and only if is a multiple of . We write to indicate that is congruent to modulo .
ii) Definition: An integer is a greatest common divisor of and , if all these conditions are satisfied:
1. is a positive integer.
2. and .
3. and imply .
iii) If , and , then .
iv) Theorem: Cancellation Law:
If and , then .
Let and , where
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