Question

when K divided by M, the remainder is 7 When K2 is divided by M, the remainder is 1 What is the maximum value of m?​

Answer 1

Answer:

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Step-by-step explanation:

ince k mod 7 = 6,

k = 7m+6, where m is an integer.

So k+2 = 7m+6+2 = 7m+8 = 7m+7+1 = 7(m+1)+1.

Let n = m+1.

Then k+2 = 7n+1.

Since m is an integer, n is an integer.

So (k+2) mod 7 =1.

The answer is 1.

Answer 2

Given:

$\frac{K}{M} = 7$ ---------- (1), and

$\frac{K^{2}}{M} = 1$ ---------- (2).

To Find:

The maximum value of M.

Solution:

By equation (1),

$M = \frac{K}{7}$

By equation (2),

$M = \frac{K^{2} }{1}$.

By equating equation (1) and equation (2),

$\frac{K}{7} = \frac{K^{2} }{1}$.

$\frac{1}{7} = \frac{K}{1}$.

$K = \frac{1}{7}$.

Putting the value of K in equation (1),

$M = \frac{\frac{1}{7} }{7}$.

$M= \frac{1}{7}\frac{1}{7}$.

$M = \frac{1}{49}$.

Hence, the value of M is $\frac{1}{49}$.