A114535 - OEIS

A114535

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

%I #11 Aug 14 2021 18:54:46

%S 1,127,3367,14911

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

%C 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.

%e 127 = 64^2 - 63^2 = 7^3 - 6^3 = 2^7 - 1^7.

%Y Cf. A115783.

%K nonn,hard,more

%O 1,2

%A _Giovanni Resta_, Feb 15 2006