Find the smallest positive integer solution to the following system of congruences: x = 0 (mod 5) x = 8 (mod 11) the solution is

The smallest positive integer solution to the given system of congruences is 30.

Step-by-step explanation:

The given system of congruences is

where, m and n are positive integers.

It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as

Now, we can say that m>n because m and n are positive integers.

For n=1,

19 is not divisible by 5 so m is not an integer for n=1.

For n=2,

The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

Therefore the smallest positive integer solution to the given system of congruences is 30.

step-by-step explanation:

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step-by-step explanation: