text: 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
  
  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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explanation: The provided text is a snippet from a textbook, specifically "Elementary Number Theory" 7th Edition, and it contains a math problem and its solution. The problem asks to show that for \( n = 1, 2, \ldots, 10 \), the expression \( 5u + 4(-1)^n \) is always a perfect square. The text also includes the solution to this problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
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  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
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distilabel_metadata.content: Elementary Number Theory - 7 Edition - Chapter 14 - Problem 2
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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
  
  Step 2 of 3
  
  Step 3 of 3
  
  Unlock Textbook Solution
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a snippet from a textbook, specifically "Elementary Number Theory" 7th Edition, and it contains a math problem and its solution. The problem asks to show that for \( n = 1, 2, \ldots, 10 \), the expression \( 5u + 4(-1)^n \) is always a perfect square. The text also includes the solution to this problem.
  
  Label: question-and-answer