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Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer?
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Show that one and only one out of n,n+2or n+4 is divisible by 3,where ...
We know that any positive integer is of the form 3q,3q+1,3q+2 for some integer q #CASE 1When n =3q , is divisible by 3 n+2= 3q+2 , is not divisible by 3 as it leaves a remainder 2n+4 = 3q+4, 3q + 3 +1, 3(q+1)+1, not divisible by 3 as it leaves a remainder 1Therefore n is divisible by 3 and n+2 and n+4 are not divisible by 3.#CASE 2n= 3q +1 noy divisible by 3 because it leaves a remainder 1n+2= 3q+1+2, 3q+3, 3(q+1) , divisible by 3 n + 4 = 3q+1+4 , 3q+5 , 3q +3+2,3(q+1)+2 ,not divisible by 3 because it leavesa remainder 2Therefore n +2 is divisible by 3 and n and n+4 are not divisible by 3CASE 3n=3q+2 ,not divisible by 3 because it leaves a remainder 2n+2= 3q+2+2 , 3q+4 , 3q + 3+1, 3 (q+1)+1 ,not divisible by 3 as it leaves a remainder 1 n+4=3q+2+4, 3q+6 ,3(q+2),divisible by 3 Therefore n+4 is divisible by 3 but n and n +2 are not divisible by 3*Therefor only one out of n , n+2, n+4 is divisible by 3 *
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Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer?
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Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer?.
Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that one and only one out of n,n+2or n+4 is divisible by 3,where n is any positive integer?.
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