Competition problem — Number theory

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Number theory Difficulty 6.3 National olympiad Find the answer

10. If you have already found the solution to the congruence equation $a x \equiv b(\bmod m)$ , how can you use this to find the solution to the linear Diophantine equation $a x + m y = b$ ? Use the problems (i), (iii), (v), (vii) from Question 1 as examples to illustrate how to find the solutions to the corresponding linear Diophantine equations.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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None

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