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Pairs of Power Numbers
Posted:
Jun 28, 2013 9:02 PM


There are many pairs of power numbers of the form a^(2n) and (a+1)^(2n) which have equal sums of digits. The simplest pair for a=4 and n=1 which gives us 4^2 = 16 and 5^2 = 25. For both the sum of digits = 7. Two more examples: a = 3154, n=7, sum of digits = 214; a = 4093, n = 30, sum of digits = 1063. If the form of the power numbers is a^(2n+1) and (a+1)^(2n+1) then there are no pairs of power numbers which have equal sums of digits. Has anyone such a pair? Or does anyone know a proof that it is impossible to find such pairs? Gerhard



