

A114535


Numbers that can be represented as (m+1)^k  m^k in at least 3 ways, with k, m > 0.


0




OFFSET

1,2


COMMENTS

The decompositions for 1 are infinite and trivial, obtained letting k=1 and m arbitrary. The representations for the other entries are 127 = 64^2  63^2 = 7^3  6^3 = 2^7  1^7, 3367 = 1684^2  1683^2 = 34^3  33^3 = 4^6  3^6, 14911 = 7456^2  7455^2 = 71^3  70^3 = 16^4  15^4. Apparently there are no other solutions < 10^9.


LINKS



EXAMPLE

127 = 64^2  63^2 = 7^3  6^3 = 2^7  1^7.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



