For some positive integer k both 4^k and 5^k start with the same digit x in base 10 i.e. 4^k = x..... 5^k = x..... What is the sum of all possible values of x.
6
The first k=11, x=2, then for the k=21/31/41, x=4, then for k= 52/62/72/82/92, x=2, starting from k=102, x=4 and so on cycles of 2 and 4. Possible value of x=2 & 4 and sum of them = 6
Let a be a single-digit positive integer. Let n be another positive integer that adjusts itself so that the unit's place digits of n and an + 1 are the same. Find the sum of all possible values of a.
A positive integer N leaves the same remainder of 35 when divided by both 2009 and 2010.
What is the remainder when N is divided by 42?
