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38. Show that one and only one out of n,+4,n+8, n+12 and n+ 16 is divisible by5, where n is any positive integer, |
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Answer» Let n be any positive integer and b = 3n = 3q+rwhere q is the quotient and r is the remainder0<r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1, 3q+2 CASE-1If n=3qn+4=3q+4n+2=3q+2here n is only divisible by 3 CASE 2If n=3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3 CASE 3If n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3 Hence it is justified that one and only one among n, n+2, n+4 is divisible by 3 in each case. |
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