Find the smallest positive integer solution to the following system of congruences: x -= 1(mod5) x -= 10(mod11)
Ernstfalld
Answered question
2021-02-10
Answer & Explanation
Nichole Watt
Skilled2021-02-11Added 100 answers
Step 1
Given that the congruence system is
The congruence means if x is divided by 6 the remainder is 1.
So number x is one of the numbers in the list:
6,11,16,21,26,31,33,41,...
Step 2
Similarity, the congruence means if x is divided by 11 the remainder is 10.
Thus, one of the numbers in the list is x:
21,32,43,54,65,76,87,98,...
The smallest number that is found in both the list is 21.
Hence, the solution to the given system of congruence is 21.
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