find the smallest number that leaves a remainder of 4 on division by 5
Find the smallest number that leaves a remainder of 4 on division by 5
Answer: To find the smallest number that leaves a remainder of 4 when divided by 5, we need to understand the concept of modular arithmetic. The problem can be formulated as finding the smallest number ( x ) such that:
x \equiv 4 \pmod{5}
This means that when ( x ) is divided by 5, the remainder is 4.
To solve this, we start by considering the general form of numbers in this congruence. Any number that satisfies this condition can be written in the form:
x = 5k + 4
where ( k ) is an integer.
To find the smallest positive ( x ), we set ( k = 0 ):
x = 5 \cdot 0 + 4 = 4
Therefore, the smallest number that leaves a remainder of 4 when divided by 5 is \boxed{4} .
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