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Solving Inequalities

If n is an in...

Question

If n is an integer, then every integral multiple of 3 can be represented by the expression ___.

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Solution

Given n is an integer. If we are to consider positive integers, then n = 1,2,3,4,5....

If we consider the expression '3n', we will have $3 \times 1, 3 \times 2, 3 \times 3$ and so on.
These numbers are positive multiples of 3.

Thus for any integer n, 3n is an integral multiple of 3.

Thus, 3n will represent an integral multiple of 3.

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Similar questions

Q. Given n is an integer, then every integral multiple of 3 can be represented by the expression___.

Q. Assertion :If

n

is an odd integer greater than 3 but not a multiple of 3, then

(x + 1)^{n} - x^{n} - 1

is divisible by

x^{3} + x^{2} + x

n

is an odd integer greater than

3

but not a multiple of

3

(1 + ω^{n} + ω^{2 n}) = 0

Q. Statement 1: If n is an odd integer greater than 3 but not a multiple of 3, then

(x + 1)^{n} - x^{n} - 1

is divisible by

x^{3} + x^{2} + x

.
Statement 2: If n is an odd integer greater than 3 but not a multiple of 3, we have

1 + ω^{n} + ω^{2 n} = 3

.

m

is said to be related to another integer

n

m

is a multiple of

n

. Then the relation is

A = [\begin{matrix} 3 & - 4 1 & - 1 \end{matrix}]

then for every integer n

A^{n}

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