Lucky number 30x0y03!
Find the value of and in the number where is the smallest and it is divisible by 13.
Insert your answer as .
The answer is 8.
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1 solution
Our number is 3000003+10000x+100y. Lets call it N. Reducing N mod 13, we get, N~6+3x+9y=3(2+x+3y), we can drop the factor 3 cu its relatively prime to 13. Thus N~2+x+3y, for min value of N, x=0. Hence N~2+3y, for y=8, we see N~26 in mod 13, which means it's divisible by 13. Thus we have x=0,y=8 as our solution
Note: a mod b means the remainder after dividing a by b.