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Can a number plus its reverse have only odd digits

Source: Nordic MO 2011 Q1

April 21, 2013
number theory unsolvednumber theory

Problem Statement

When a0,a1,…,a1000a_0, a_1, \dots , a_{1000} denote digits, can the sum of the 10011001-digit numbers a0a1⋯a1000a_0a_1\cdots a_{1000} and a1000a999⋯a0a_{1000}a_{999}\cdots a_0 have odd digits only?
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