You need to use the definition of congruence such that:

`x^37 -= 12` mod 5 if `5| (x^37 - 12)`

Notice that this is not a linear congruence but you may try x = 0, x= 1, ...., x = 4.

`x = 1 =gt 5` does not divide 11

`x = 2 =gt 2^37 - 12` is not divisible by 5

`x = 3 =gt 3^37 - 12` is not divisible by 5

`x = 4 =gt 4^37 - 12` is not divisible by 5

**Hence, there are not x integer values to satisfy the congruence equation.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now