Let be the value of the expression above. Find the last two digits of
Given that in the 8-digit number ,
(i)
(ii) The numbers and are both divisible by .
Let the sum of all possible values of be .
Find the digit sum of .
Details and assumptions:-
Consider the sequence for positive integer :
If we take the greatest common divisor of 2 consecutive terms, we obtain
What is the sum of all distinct elements in the second series?
If we write out the decimal expansion of the smaller root of , we get the following decimal: which we notice as the first 5 Catalan numbers. How many distinct Catalan numbers occur in a row before this pattern stops?
Let be positive integers that satisfy the equation above. Find the maximum possible value of .