Originally Posted by fring
Keep Smiling
Malay
When a positive integer N is written in base 6 , it is a four digit number such that all its four digits are the same. When N is written in base ten, it is a three digit number such that all its three digits are equal. Find the decimal representations of all such numbers N.
Please help!!!!!!!! desperate!!!! THAANK YOU!!!!
Hello, fring!
I will assume that you know something about number bases.
Otherwise, you shouldn't be trying problems like this . . .
When a positive integer N is written in base 6 , it is a 4-digit number such that all its digits are equal.
When N is written in base ten, it is a 3-digit number such that all its digits are equal.
Find the decimal representations of all such numbers N.
In base-6:
In base-10:
Hence: .
Since is a digit in base-6 and is a digit in base-10,
. . the only solution is:
Therefore: .