Two maths lovers Parth and Pranjal competed each other for the number of problems solved correctly in days streak at Brilliant.
Let be the number of problems solved by Parth on the day.
Let be the number of problems solved by Pranjal on the day.
Note: can be rational numbers , since there may be some questions which both may have solved partially.
The two sequences and are non-decreasing . The competition was tough , and Pranjal won by problem.
What is the minimum value of ?
Note: (taxicab number) , are two consecutive sphenic numbers.