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Marianna [84]
3 years ago
10

Prove: If n is a positiveinteger and n2 is divisible by 3, then n is divisible by3.

Mathematics
1 answer:
notka56 [123]3 years ago
5 0

Answer:

If n^2 is divisible by 3, the n is also divisible by 3.

Step-by-step explanation:

We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, n^2 is not divisible by 3.

Let n not be divisible by 3. Then \frac{n}{3} can be written in the form of fraction \frac{x}{y}, where x and y are co-prime to each other or in other words the fraction is in lowest form.

Now, squaring

\frac{n^2}{9} = \frac{x^2}{y^2}

Thus,

n^2 = \frac{9x^2}{y^2}

\frac{n^2}{3} = \frac{3x^2}{y^2}

It can be clearly seen that the fraction \frac{3x^2}{y^2} is in lowest form.

Hence, n^2 is not divisible by 3.

Thus, by contrapositivity if n^2 is divisible by 3, the n is also divisible by 3.

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