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?

Question

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?

anonymous · Answer

11

myininaya · Answer

gj how did you go about it?

anonymous · Answer

I just tried consecutive multiples of 5

myininaya · Answer

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