2. Solve the following polynomial congruences. ces (a) x² + 12x – 17 = 0 (mod 143) (b) x³ + 30x² + 27x + 23 = 0 (mod 45)

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Chapter2: Second-order Linear Odes
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Can you do #2?
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
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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