lease help with number 2. A. B.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 18E
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Please help with number 2. A. B. C.
Clon 11.3
adtice the divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10 on these numbers:
b. 700010154
Give a six-digit number that meets each of the following criteria:
а. 43056
c. 9460000000023
d. 71005165
2 and 3 are factors of the number, but 4 and 9 are not.
b. 3 and 5 are factors of the number, but 10 is not.
c. 8 and 9 are factors of the number.
3. What digit could represent in n = 41870432 if 3 is a factor of n? If 9 is a factor
of n? Give all the single-digit possibilities for D.
monto
4. Notice that 2 and 4 are factors of 12, but 2 · 4, or 8, is not. So a divisibility test for 8
that is not safe is to use the 2 test and the 4 test. Find counterexamples for these
plausible-looking but unreliable divisibility tests.
a. 12 is a factor of n if and only if 2 is a factor of n and 6 is a factor of n.
b. 18 is a factor of n if and only if 3 is a factor of n and 6 is a factor of n.
C. 24 is a factor of n if and only if 4 is a factor of n and 6 is a factor of n.
a. 10 is a factor of n if and only if 2 is a of n and 5 is a factor of n.
nd only if 3 is a factor of n and 4 is a factor of n.
y the conjectured divisibility tests in parts (a-d), with 3 or 4 examples each.
Transcribed Image Text:Clon 11.3 adtice the divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10 on these numbers: b. 700010154 Give a six-digit number that meets each of the following criteria: а. 43056 c. 9460000000023 d. 71005165 2 and 3 are factors of the number, but 4 and 9 are not. b. 3 and 5 are factors of the number, but 10 is not. c. 8 and 9 are factors of the number. 3. What digit could represent in n = 41870432 if 3 is a factor of n? If 9 is a factor of n? Give all the single-digit possibilities for D. monto 4. Notice that 2 and 4 are factors of 12, but 2 · 4, or 8, is not. So a divisibility test for 8 that is not safe is to use the 2 test and the 4 test. Find counterexamples for these plausible-looking but unreliable divisibility tests. a. 12 is a factor of n if and only if 2 is a factor of n and 6 is a factor of n. b. 18 is a factor of n if and only if 3 is a factor of n and 6 is a factor of n. C. 24 is a factor of n if and only if 4 is a factor of n and 6 is a factor of n. a. 10 is a factor of n if and only if 2 is a of n and 5 is a factor of n. nd only if 3 is a factor of n and 4 is a factor of n. y the conjectured divisibility tests in parts (a-d), with 3 or 4 examples each.
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