2. Solve the following polynomial congruences. ces (a) x² + 12x – 17 = 0 (mod 143) (b) x³ + 30x² + 27x + 23 = 0 (mod 45)
2. Solve the following polynomial congruences. ces (a) x² + 12x – 17 = 0 (mod 143) (b) x³ + 30x² + 27x + 23 = 0 (mod 45)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Can you do #2?
Transcribed Image Text:4 Polynomial Congruences
(c) r³ + 5x² + 2x - 1 = 0 (mod 7²)
2. Solve the following polynomial congruences.
ccessful on
(a) x² + 12x – 17 = 0 (mod 143)
(b) x³ + 30x² +27x + 23 = 0 (mod 45)
meth
aga2000
3. Determine, without using a computer, all integers
digits of x are the same as those of x.
4. Let m = pi.pk. Suppose the congruence fº
ni distinct solutions for 1 < i < k. Show that f
nin2..nk distinct solutions.
3. Let p be an odd prime. Show that x² = 1 (mod pª
tions for any k>1.
a1
0. Let p be an odd prime. Show that x2 = a (mod p*),
solutions if x2 = a (mod p) has two solutions, and
(mod p) has no solutions.
1. This ou
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