21st Putnam 1960

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Problem B4

Show that if an (infinite) arithmetic progression of positive integers contains an nth power, then it contains infinitely many nth powers.

 

Solution

Let the difference between adjacent terms of the progression be d. Suppose that Nn is an nth power in the progression. Then (N+d)n is a larger nth power in the progression (it is obvious from the binomial expansion that it has the form N + kd).

 


 

21st Putnam 1960

© John Scholes
jscholes@kalva.demon.co.uk
25 Jan 2002