Is N2-1 Divisible by 8 if N is?

Explaining the Theory

The question of whether or not N2-1 is divisible by 8 if N is can be answered by breaking down the equation and understanding the theory behind it. N2-1 is an expression that is composed of two terms: N2 and -1. N2 is the result of a number N, multiplied by itself. The second term of the equation, -1, is an integer that is negative one.

In order to determine if N2-1 is divisible by 8, one must first understand the concept of divisibility. In mathematics, divisibility is defined as the ability of an integer (or number) to be divided by another number without a remainder. For example, the number 8 is divisible by 4, because 8 divided by 4 is equal to 2 with no remainder.

Can N2-1 be Divided by 8?

Now that the basics of divisibility have been established, the question can be answered: can N2-1 be divided by 8? The answer is yes, N2-1 can be divided by 8 if N is divisible by 4. This is because when N2-1 is divided by 8, the remainder is always 0.

This is due to the fact that N2-1 is composed of two terms: N2 and -1. N2 is divisible by 8, because when N is divisible by 4, N2 is also divisible by 8. The second term of the equation, -1, is an integer that is negative one, and is also divisible by 8. Therefore, when both terms are combined, the result is that N2-1 is divisible by 8 if N is divisible by 4.

Conclusion

To conclude, N2-1 is divisible by 8 if N is divisible by 4. This is because when N2-1 is divided by 8, the remainder is always 0. Understanding the basics of divisibility and breaking down the equation can help one determine if N2-1 is divisible by 8 if N is.

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