This preview shows page 1. Sign up to view the full content.
MAT 312/AMS 351 – Fall 2010
Homework 5
1. Explain in your own words why, if
n
is a prime, a linear congruence
equation
ax
≡
n
b
always has a solution (i.e that given any integers
a
and
b
, there exists an integer
x
such that
ax
−
b
is a multiple of
n
), and
that any two solutions are the same modulo
n
.
2. Solve 3
x
≡
19
16.
Not
by trialanderror please.
3. Solve 5
x
≡
14
12 (14 not prime, but (5,14) = 1 suFcient).
4. Review the procedure for the case (
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: a, n ) = d n = 1. 5. Explain why 6 x ≡ 21 2 has no solutions. 6. Show that 6 x ≡ 21 9 if and only if 2 x ≡ 7 3. 7. Solve 2 x ≡ 7 3. Let x be the unique solution. 8. Check that x , x 1 = x + 1 · 7 and x 2 = x + 2 · 7 are all diferent solutions of 6 x ≡ 21 9. Why does this not work for x + 3 · 7? 9. ±ind the seven solutions of 14 x ≡ 35 21. 1...
View
Full
Document
This note was uploaded on 12/14/2010 for the course AMS 94303 taught by Professor Anthonyphillips during the Fall '10 term at SUNY Stony Brook.
 Fall '10
 AnthonyPhillips

Click to edit the document details