myininaya
  • myininaya
i have a fun question. it took a few minutes to think about and get... Let n be a positive integer. If n is divided by 3, the remainder is 2 and if n is divided by 5, the remainder is 1. What is the smallest n with the above conditions?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
11
myininaya
  • myininaya
gj how did you go about it?
anonymous
  • anonymous
I just tried consecutive multiples of 5

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myininaya
  • myininaya
i did n/3=q1+2/3 -> n=3q1+2 n/5=q2+1/5 -> n=5q2+5 so 3q1+2=5q2+1 3q1-5q2=1-2 3q1-5q2=-1 5q2-3q1=1 5=3(1)+2 3=2(1)+1 2=2(1) 1=3-2 1=3-(5-3) 1=2(3)-5(1) 1=2(3)+5(-1) 1=2(3)+5(2-3) 1=2(3)+5(2)-5(3) 1=-3(3)+5(2) so q1=3 and q2=2 so n=3q1+2=3(3)+2=11

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