- #1
teng125
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anyone pls help...for this ques:For any natural number n, n^3 + 2n is divisible by 3.
i don't know how to start or do
i don't know how to start or do
This statement means that for any natural number, when it is raised to the third power and added to twice itself, the resulting number is divisible by 3. In other words, the remainder when dividing n^3 + 2n by 3 is always 0.
This statement was proven using mathematical induction. The base case (n=1) was shown to be true, and then it was shown that if the statement holds for n, it also holds for n+1. Therefore, the statement holds for all natural numbers.
This statement is significant because it is a fundamental property of natural numbers and can be used in various mathematical proofs and applications. It also demonstrates the power of mathematical induction as a proof technique.
No, this statement only holds for natural numbers. If n is a negative number, n^3 + 2n will not be divisible by 3. Additionally, if n is a non-integer, the statement does not hold.
While this statement may not have a direct practical application, it is a useful property in number theory and can be used to prove other theorems and solve problems in mathematics. It also serves as a basis for understanding divisibility rules and patterns in numbers.