If P = (99^x - 99^y), where x & y can be any integer. When P is divided by 100, How many different types of reminders we can find?
a) 3 b) 2 c)1 d) 0 e) none of these
a) 3 b) 2 c)1 d) 0 e) none of these
99 can be expressed as 9*11 and ((9*11)^x-(9*11)^y)/100 is what interests us
9 raised to the different powers returns a unit's digits 1 or 9; 9 or 1 multiplied by 11 raised to any power remain their values
thus, the remainders can be 0 (or no remainder), 98, 1 resuming with 2 remainders
a
[spoiler]
my only concern is we are asked to find the types of remainders and not actual remainders, because 0 is when we have no remainder, but i include this in my final answer. Without 0 we have two types of remainders, with 0 we have 3 types.[/spoiler]
