Question

N is an square of any odd positive integer. Find the remainder when 5N+3 is divided by 20

Answer 1

Answer:

8

Step-by-step explanation:

Given that N is the square of any odd positive integer. We denote an odd positive integer as 2n + 1

So, N = (2n + 1)²

⇒ N = 4n² + 4n + 1

[using (a + b)² = a² + b² + 2ab]

We have to find the remainder when 5N + 3 is divided by 20.

Substitute the value of N in 5N + 3

$\sf \frac{5N+3}{20}\\\\\implies \frac{5(4n^2+4n+1)+3}{20}\\\\\implies \frac{20n^2+20n+5+3}{20}\\\\\implies \frac{20n^2+20n+8}{20}$

$\sf\implies\frac{20(n^2 +n) + 8}{20}\\\\\implies \frac{20(n^2+n)}{20}+\frac{8}{20}$

Clearly, 20n² + 20n would always be a multiple of 20. So the remainder would be given by the remaining term, that is 8. When 8 is divided by 20, the quotient is 0 and remainder is 8. Hence the answer is 8.

Answer 2

Answer:

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