To prove: The system of congruences x\equiv 2(\bmod 16) and x\equiv 3(\bmod 9) has no solution.

Jaya Legge

Jaya Legge

Answered question

2021-03-23

To prove: The system of congruences x2(bmod16) and x3(bmod9) has no solution.

Answer & Explanation

Pohanginah

Pohanginah

Skilled2021-03-25Added 96 answers

Given:
The system of following congruences:
x2(bmod6)...(1)
x3(bmod9)...(2)
Formula used:
The congruence:
ab(bmodm),a=km+b
Proof:
Consider the system of following congruences:
x2(bmod6)...(1)
x3(bmod9)...(2)
The equations (1) and (2) implies that
x=6p+2 and x=9q+3
Let us consider
x=9q+3
=3(3q+1)
Here, x is divisible by 3.
Now, consider
x=6p+2
=2(3p+1)
Here, x is divisible by 2 but not by 3.
Thus, it is proved that the system of congruences x2(bmod6) and x3(bmod9) has no solution.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?