Find the number of integer solutions of 3 x - 1 15-A- 0B- 1C- 2D- 3

The correct option is A 03x ≡ 1(mod 15) 3x − 1= 15k for some integer k 3x= 15k+1 x= 15k/3+1/3 x= 5k+1/3 Since 5k is an integer, 5k+1/3 is not an integer. So ...

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Standard X

Mathematics

Modular Arithmetic and Congruence Modulo

Find the numb...

Question

Find the number of integer solutions of $3 x \equiv 1 (m o d 15)$ .

0.0

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Solution

The correct option is A 0.0
$3 x \equiv 1 (m o d 15)$

$3 x - 1 = 15 k$ for some integer k
$3 x = 15 k + 1$
$x = \frac{15 k}{3} + \frac{1}{3}$
$x = 5 k + \frac{1}{3}$
Since 5k is an integer, $5 k + \frac{1}{3}$ is not an integer.
So there is no integer solution.

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Find the number of integer solutions of 3x≡1(mod 15).

The correct option is A 0.03x≡1(mod 15) 3x − 1=15k for some integer k 3x=15k+1 x=15k3+13 x=5k+13 Since 5k is an integer, 5k+13 is not an integer. So there is no integer solution.

Find the number of integer solutions of $3 x \equiv 1 (m o d 15)$ .

The correct option is A 0.0
$3 x \equiv 1 (m o d 15)$

$3 x - 1 = 15 k$ for some integer k
$3 x = 15 k + 1$
$x = \frac{15 k}{3} + \frac{1}{3}$
$x = 5 k + \frac{1}{3}$
Since 5k is an integer, $5 k + \frac{1}{3}$ is not an integer.
So there is no integer solution.