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37th Austrian Mathematical Olympiad 2006

Source: round2, problem1

February 10, 2009
functionnumber theory unsolvednumber theory

Problem Statement

Let n n be a non-negative integer, which ends written in decimal notation on exactly k k zeros, but which is bigger than 10k 10^k. For a n n is only k\equal{}k(n)\geq2 known. In how many different ways (as a function of k\equal{}k(n)\geq2) can n n be written as difference of two squares of non-negative integers at least?
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