A problem by Josh Rowley

Level pending

You are given that 101760 = 1 9 4 19^{4} - 1 3 4 13^{4} . How many different possible non-negative integer values are there for r , r 728 r\le 728 , for which the congruence 101760 k r ( m o d 729 ) 101760k\equiv r \pmod{729} has a solution for some positive integer k ?


The answer is 243.

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