4th CaMO 1972 Problem 3 Show that 10201 is composite in base n > 2. Show that 10101 is composite in any base.
Solution
Let the base be b, then 10201 = (b 4 + 2b 2 + 1) = (b 2 + 1) 2 = 101 2 . 10101 = (b 4 + 2b 2 + 1) - b 2 = (b 2 + b + 1)(b 2 - b + 1). We have b > 1, so each factor is > 1. 4th CaMO 1972 © John Scholes [email protected] 10 June 2002
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