SOLUTION: 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

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Question 41506This question is from textbook
: 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. This question is from textbook

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
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.
natural number could be
case 1...even....=2m
its square=2m*2m=4m^2...divisible by 4
case 2....odd.....2m-1
its square =(2m-1)^2=4m^2-4m+1=4(m^2-m)+1=4k+1...where k is an integer.
hence square of every natural number is either a multiple of 4 or leaves a remainder of 1 when divided by 4.