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18th ibmo - argentina 2003/q6

Source: Spanish Communities

April 9, 2006
quadraticsinductionmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

The sequences (an),(bn)(a_n),(b_n) are defined by a0=1,b0=4a_0=1,b_0=4 and for n≥0n\ge 0 an+1=an2001+bn,  bn+1=bn2001+ana_{n+1}=a_n^{2001}+b_n,\ \ b_{n+1}=b_n^{2001}+a_n Show that 20032003 is not divisor of any of the terms in these two sequences.
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