document.write( "Question 41506This question is from textbook
\n" ); document.write( ": A student has noticed that every squared natural number is either a multiple of 4 or one larger than a multiple of 4, but isn't sure if this is always tru. Use algebraic reasoning to explain to the student why this is always tru. \n" ); document.write( "

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A student has noticed that every squared natural number is either a multiple of 4 or one larger than a multiple of 4, but isn't sure if this is always tru. Use algebraic reasoning to explain to the student why this is always tru.
\n" ); document.write( "natural number could be
\n" ); document.write( "case 1...even....=2m
\n" ); document.write( "its square=2m*2m=4m^2...divisible by 4
\n" ); document.write( "case 2....odd.....2m-1
\n" ); document.write( "its square =(2m-1)^2=4m^2-4m+1=4(m^2-m)+1=4k+1...where k is an integer.
\n" ); document.write( "hence square of every natural number is either a multiple of 4 or leaves a remainder of 1 when divided by 4. \n" ); document.write( "

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