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given last 2-digit part of 9 numbers, find last 2-digit part of sum of squares

Source: Greece JBMO TST 2010 p1

April 29, 2019
number theorySum of SquaresalgebraDigitsDigit

Problem Statement

Nine positive integers a1,a2,...,a9a_1,a_2,...,a_9 have their last 22-digit part equal to 11,12,13,14,15,16,17,1811,12,13,14,15,16,17,18 and 1919 respectively. Find the last 22-digit part of the sum of their squares.
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