# Integers and Divisibility Challenge

• MHB
• anemone
In summary, integers are a set of numbers that includes all whole numbers and their negative counterparts, while whole numbers are a set of numbers that include only positive numbers and zero. The divisibility rule for integers states that a number is divisible by another number if the first number can be divided evenly by the second number without leaving a remainder. To determine if a number is divisible by another number, you can use the divisibility rule, factors, and divisibility tests. The "Integers and Divisibility Challenge" is designed to test and improve knowledge and understanding in this area of math. To improve skills in dealing with integers and divisibility, one can practice regularly, use online resources and tools, seek help from a tutor or teacher, and
anemone
Gold Member
MHB
POTW Director
Prove that $\dfrac{378^3+392^3+1053^3}{2579}$ is an integer.

Hint:

One can do some algebraic manipulation to the numerator and therefore factorize them.

## 1. What are integers?

Integers are whole numbers, both positive and negative, including zero. They do not have any decimal or fractional parts.

## 2. How do you determine if a number is divisible by another number?

A number is divisible by another number if the remainder is equal to zero when the first number is divided by the second number. For example, 12 is divisible by 4 because 12 ÷ 4 = 3 with no remainder.

## 3. What is the purpose of the "Integers and Divisibility Challenge"?

The purpose of this challenge is to test and improve one's understanding of integers and divisibility rules through a series of mathematical problems and puzzles.

## 4. How can I improve my skills in working with integers and divisibility?

Practice is key in improving your skills with integers and divisibility. You can also review and learn different divisibility rules and strategies to solve problems more efficiently.

## 5. Can I use a calculator for the "Integers and Divisibility Challenge"?

It is recommended to solve the challenge without a calculator as it will help improve your mental math skills. However, you can use a calculator if needed, but it may take away from the purpose of the challenge.

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