Question: say whether the following is true or false and support your answer by a proof: The sum of any five consecutive integers is divisible by 5 (without reminder). Answer: it's true.
Claim: the sum of any five consecutive integers is divisible by 5. Proof: let's prove it directly. Let's take an arbitrary number $n \in {Z}$. Then the sum of five consecutive integers can be presented as:
$$n+(n+1)+(n+2)+(n+3)+(n+4) = 5n+10 = 5(n+2)$$
By the definition of divisibility $5(n+2)$ is divisible by 5, so the sum of any five consecutive integers is divisible by 5. $\blacksquare$
**Question**: say whether the following is true or false and support your answer by a proof: The sum of any five consecutive integers is divisible by 5 (without reminder).
**Answer**: it's true.
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**Claim**: the sum of any five consecutive integers is divisible by 5.
**Proof**: let's prove it directly. Let's take an arbitrary number $n \in {Z}$. Then the sum of five consecutive integers can be presented as:
$$n+(n+1)+(n+2)+(n+3)+(n+4) = 5n+10 = 5(n+2)$$
By the definition of divisibility $5(n+2)$ is divisible by 5, so the sum of any five consecutive integers is divisible by 5. $\blacksquare$