+49 complete \(2011 \cdot 2012 \cdot 2013 \cdot 2014 \) modulo 5.
and
in this problem, a and b are positive integers.
When a is written in base 9, its last digit is 5.
When b is written in base 6, its last two digits are 53.
When a-b is written in base 3, what are its last two digits? Assume a-b is positive.
You can have an infinite number of solutions:
We can choose "a" to be 140 in base ten = 165 in base 9
We can choose "b" to be 105 in base ten = 253 in base 6
Now, we can convert 140 and 105 from base 10 to base 3:
140 in base 10 =1 2012 in base 3, and:
105 in base 10 =1 0220 in base 3. So:
1 2012 - 1 0220 =1022 in base 3.
