Elementary Number Theory - 7 Edition - Chapter 14 - Problem 2
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# For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

Elementary Number Theory | 7th Edition

Problem 2

For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

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Week 1 BASICS REWIEW Arithmetic:  a+b=b+a  a+b +c=a+(b+c)  ab+c =ab+ac  ab=ba  ab)c=a(bc) Multiplying Fractions: a c ac  × = b d bd Dividing Fractions:  a÷ = ad b d bc Adding Fractions: a+ = ad+cb= ad+bc  b d bd bd bd Exponent Basics:  an means multiply a by itself n times  0 =0wheren>0 0  a =1wherea≠0  0 isindeterminate a = 1 wherea≠0  an becau0e n−n n −n 1=a =a =a a 1=a a−n 1 =a−n an Laws of Exponents: Given m & n are integers and a & b are real numbers:  a a =a m+n m a m−n  n =a wherea≠0 a

###### Chapter 14, Problem 2 is Solved

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The text passage contains a mathematical problem from a textbook, asking to show that a specific expression is always a perfect square for a given range of n. The solution to this problem is also provided in the text.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Elementary Number Theory - 7 Edition - Chapter 14 - Problem 2
Register Now

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Get Full Access to Elementary Number Theory - 7 Edition - Chapter 14 - Problem 2

9780073383149

# For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

Elementary Number Theory | 7th Edition

Problem 2

For n = 1, 2, ... , 10, show that 5u + 4(-l)n is always a perfect square

Accepted Solution
Step-by-Step Solution:
Step 1 of 3

Week 1 BASICS REWIEW Arithmetic:  a+b=b+a  a+b +c=a+(b+c)  ab+c =ab+ac  ab=ba  ab)c=a(bc) Multiplying Fractions: a c ac  × = b d bd Dividing Fractions:  a÷ = ad b d bc Adding Fractions: a+ = ad+cb= ad+bc  b d bd bd bd Exponent Basics:  an means multiply a by itself n times  0 =0wheren>0 0  a =1wherea≠0  0 isindeterminate a = 1 wherea≠0  an becau0e n−n n −n 1=a =a =a a 1=a a−n 1 =a−n an Laws of Exponents: Given m & n are integers and a & b are real numbers:  a a =a m+n m a m−n  n =a wherea≠0 a

###### Chapter 14, Problem 2 is Solved

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Unlock Textbook Solution
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The text passage contains a mathematical problem from a textbook, asking to show that a specific expression is always a perfect square for a given range of n. The solution to this problem is also provided in the text.

TYPE: SINGLE_QUESTION_WITH_ANSWER