 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/discrete-mathematics-continuous-mathematics-and-probability/1/a/solution

754 = 8 \cdot 91 + 26, - 507 = - 6 \cdot 91 + 39.

More explicitly,

754 x + 507 = 91 (8 x + 6) + (26 x - 39) .

The first expression is divisible by

91

exactly when the last parenthesis is. By the definition of a integer congruence, the two congruences are equivalent.

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