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Huge perfect squares and 17-th dgits

Source: All-Russian MO Round 4

April 2, 2005
inequalitiesnumber theory proposednumber theory

Problem Statement

11.7 Let NN be a number of perfect squares from {1,2,...,1020}\{1,2,...,10^{20}\}, which 17-th digit from the end is 7, and MM be a number of perfect squares from {1,2,...,1020}\{1,2,...,10^{20}\}, which 17-th digit from the end is 8. Compare MM and NN. (A. Golovanov)
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