N + 4 = 5 * (5/4)^5 (F + 1), and so N = (5^6/4^5)(F + 1) – 4, and so on. ]]>

Another way to arrive at that answer is to add 4 to each equation:

N + 4 = 5(A + 1)

4(A + 1) = 5(B + 1)

4(B + 1) = 5(C + 1)

4(C + 1) = 5(D + 1)

4(D + 1) = 5(E + 1)

4(E + 1) = 5(F + 1)

Thus N + 4 = (5/4)^5 (F + 1), and so N = (5^5/4^5)(F + 1) – 4.

5^5/4^5 is a fraction in is lowest terms, so the only way N can be an integer is if F + 1 is a multiple of 4^5.

So the general solution is N = 15625t – 4, where t is a positive integer.

Thus, as you found, the smallest solution is 15621.

To delete a comment, just log in, and view the posts’ comments, there you will have the option to edit or delete them. ]]>