banganX

2021-02-21

To find: The smallest positive integer that solves the congruences

### Answer & Explanation

Given information:
The congruences
Consider the given congruences

‘The congruence means if x is divided by 7, the remainder is 3.
So the number x is one of the numbers in the following list:
3, 10, 17, 24, 31, 38, 45, -
Similarly, the congruence means if x is divided by 5, the remainder is 4.
So the number x is one of the numbers in the following list:
4,9, 14, 19,24, 29,34, 39, 44, -
The smallest number that is found in both the lists is 24, so the
smallest number that solves the congruences
is 24.
$⇒x=24$
Final Statement:
The smallest positive integer that solves the congruences
is x = 24.

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