Question-168538

Question Number 168538 by Mastermind last updated on 12/Apr/22

Answered by mr W last updated on 12/Apr/22

N = 7 a + 3 = 4 b + 2

4 b - 7 a = 1

\Rightarrow b = 7 k + 2

\Rightarrow N = 4 (7 k + 2) + 2 = 28 k + 10

k = 0, 1, \dots, 35 \Rightarrow 36 n u m b e r s

Commented by Tawa11 last updated on 12/Apr/22

Great sir .

Commented by Mastermind last updated on 13/Apr/22

T h a n k s {m a n}^{'} l o v e y o u g u y s

Commented by otchereabdullai@gmail.com last updated on 13/Apr/22

great

Answered by mathfreak last updated on 12/Apr/22

x = 3 m o d 7 = 7 a + 3

x = 2 m o d 4 = 4 b + 2

4 x = 28 a + 12

7 x = 28 b + 14

7 x - 4 x = 28 (a - b) + 2

3 x = 28 c + 2

\Rightarrow 3 x = 28 (3 d + 1) + 2

3 x = 84 d + 30

x = 28 d + 10

x = {28 (0) + 10, 28 (1) + 10, \dots, 28 (35) + 10}

n {(x)}_{0 < x < 1000} = 35 + 1 = 36

Commented by Tawa11 last updated on 12/Apr/22

Great sir .

Commented by Mastermind last updated on 13/Apr/22

T h a n k s, {y o u}^{'} r e e x t r e m e l y d i d a g r e a t j o b