Question

Determine whether the congruence is true or false.
12 ≡ 10 mod 5

Answer 1

The given congruence is false.

Explanation:

Given : Expression
`12 \equiv 10 \mod 5`

To find : Determine whether the congruence is true or false ?

Solution :

The congruence is in the form
`x\mod y\equiv r`

where, x is the dividend

y is divisor

r is the remainder

So, We find
`10 \mod 5`

We know, 10 is completely divide by 5 and we get quotient is 2 and remainder is 0.

`10 \mod 5=0`

As
`0\\eq 12`

Therefore, The given congruence is false.